Precálculo Ejemplos

$\cot (x) \sec^{4} (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1

Simplifica el lado izquierdo.

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Paso 1.1

Simplifica $\cot (x) \sec^{4} (x)$ .

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Paso 1.1.1

Reescribe $\cot (x)$ en términos de senos y cosenos.

$\frac{\cos (x)}{\sin (x)} \sec^{4} (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.2

Reescribe $\sec (x)$ en términos de senos y cosenos.

$\frac{\cos (x)}{\sin (x)} {(\frac{1}{\cos (x)})}^{4} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.3

Simplifica la expresión.

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Paso 1.1.3.1

Aplica la regla del producto a $\frac{1}{\cos (x)}$ .

$\frac{\cos (x)}{\sin (x)} \cdot \frac{1^{4}}{\cos^{4} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.3.2

Uno elevado a cualquier potencia es uno.

$\frac{\cos (x)}{\sin (x)} \cdot \frac{1}{\cos^{4} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.4

Multiplica $\frac{\cos (x)}{\sin (x)}$ por $\frac{1}{\cos^{4} (x)}$ .

$\frac{\cos (x)}{\sin (x) \cos^{4} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.5

Cancela el factor común de $\cos (x)$ y $\cos^{4} (x)$ .

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Paso 1.1.5.1

Multiplica por $1$ .

$\frac{\cos (x) \cdot 1}{\sin (x) \cos^{4} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.5.2

Cancela los factores comunes.

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Paso 1.1.5.2.1

Factoriza $\cos (x)$ de $\sin (x) \cos^{4} (x)$ .

$\frac{\cos (x) \cdot 1}{\cos (x) (\sin (x) \cos^{3} (x))} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.5.2.2

Cancela el factor común.

$\frac{\cos (x) \cdot 1}{\cos (x) (\sin (x) \cos^{3} (x))} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.5.2.3

Reescribe la expresión.

$\frac{1}{\sin (x) \cos^{3} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.6

Separa las fracciones.

$\frac{1}{\cos^{3} (x)} \cdot \frac{1}{\sin (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.7

Convierte de $\frac{1}{\sin (x)}$ a $\csc (x)$ .

$\frac{1}{\cos^{3} (x)} \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.8

Combina $\frac{1}{\cos^{3} (x)}$ y $\csc (x)$ .

$\frac{\csc (x)}{\cos^{3} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.9

Factoriza $\cos (x)$ de $\cos^{3} (x)$ .

$\frac{\csc (x)}{\cos (x) \cos^{2} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.10

Separa las fracciones.

$\frac{1}{\cos^{2} (x)} \cdot \frac{\csc (x)}{\cos (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.11

Reescribe $\csc (x)$ en términos de senos y cosenos.

$\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\sin (x)}}{\cos (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.12

Reescribe $\frac{\frac{1}{\sin (x)}}{\cos (x)}$ como un producto.

$\frac{1}{\cos^{2} (x)} (\frac{1}{\sin (x)} \cdot \frac{1}{\cos (x)}) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.13

Simplifica.

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Paso 1.1.13.1

Convierte de $\frac{1}{\sin (x)}$ a $\csc (x)$ .

$\frac{1}{\cos^{2} (x)} (\csc (x) \frac{1}{\cos (x)}) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.13.2

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$\frac{1}{\cos^{2} (x)} (\csc (x) \sec (x)) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.14

Reescribe $1$ como $1^{2}$ .

$\frac{1^{2}}{\cos^{2} (x)} (\csc (x) \sec (x)) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.15

Reescribe $\frac{1^{2}}{\cos^{2} (x)}$ como ${(\frac{1}{\cos (x)})}^{2}$ .

${(\frac{1}{\cos (x)})}^{2} (\csc (x) \sec (x)) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.16

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$\sec^{2} (x) (\csc (x) \sec (x)) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.17

Multiplica $\sec^{2} (x)$ por $\sec (x)$ sumando los exponentes.

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Paso 1.1.17.1

Mueve $\sec (x)$ .

$\sec (x) \sec^{2} (x) \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.17.2

Multiplica $\sec (x)$ por $\sec^{2} (x)$ .

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Paso 1.1.17.2.1

Eleva $\sec (x)$ a la potencia de $1$ .

$\sec^{1} (x) \sec^{2} (x) \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.17.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

${\sec (x)}^{1 + 2} \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 1.1.17.3

Suma $1$ y $2$ .

$\sec^{3} (x) \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

Paso 2

Como $x$ está en el lado derecho de la ecuación, cambia los lados para que quede en el lado izquierdo de la ecuación.

$\cot (x) + 2 \tan (x) + \tan^{3} (x) = \sec^{3} (x) \csc (x)$

Paso 3

Simplifica el lado izquierdo.

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Paso 3.1

Simplifica cada término.

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Paso 3.1.1

Reescribe $\cot (x)$ en términos de senos y cosenos.

$\frac{\cos (x)}{\sin (x)} + 2 \tan (x) + \tan^{3} (x) = \sec^{3} (x) \csc (x)$

Paso 3.1.2

Reescribe $\tan (x)$ en términos de senos y cosenos.

$\frac{\cos (x)}{\sin (x)} + 2 \frac{\sin (x)}{\cos (x)} + \tan^{3} (x) = \sec^{3} (x) \csc (x)$

Paso 3.1.3

Combina $2$ y $\frac{\sin (x)}{\cos (x)}$ .

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \tan^{3} (x) = \sec^{3} (x) \csc (x)$

Paso 3.1.4

Reescribe $\tan (x)$ en términos de senos y cosenos.

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + {(\frac{\sin (x)}{\cos (x)})}^{3} = \sec^{3} (x) \csc (x)$

Paso 3.1.5

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sec^{3} (x) \csc (x)$

Paso 4

Simplifica el lado derecho.

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Paso 4.1

Simplifica $\sec^{3} (x) \csc (x)$ .

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Paso 4.1.1

Reescribe $\sec (x)$ en términos de senos y cosenos.

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = {(\frac{1}{\cos (x)})}^{3} \csc (x)$

Paso 4.1.2

Aplica la regla del producto a $\frac{1}{\cos (x)}$ .

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1^{3}}{\cos^{3} (x)} \csc (x)$

Paso 4.1.3

Uno elevado a cualquier potencia es uno.

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1}{\cos^{3} (x)} \csc (x)$

Paso 4.1.4

Reescribe $\csc (x)$ en términos de senos y cosenos.

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\sin (x)}$

Paso 4.1.5

Combinar.

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1 \cdot 1}{\cos^{3} (x) \sin (x)}$

Paso 4.1.6

Multiplica $1$ por $1$ .

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 5

Multiplica ambos lados de la ecuación por $\sin (x)$ .

$\sin (x) (\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)}) = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 6

Aplica la propiedad distributiva.

$\sin (x) \frac{\cos (x)}{\sin (x)} + \sin (x) \frac{2 \sin (x)}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7

Simplifica.

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Paso 7.1

Cancela el factor común de $\sin (x)$ .

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Paso 7.1.1

Cancela el factor común.

$\sin (x) \frac{\cos (x)}{\sin (x)} + \sin (x) \frac{2 \sin (x)}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.1.2

Reescribe la expresión.

$\cos (x) + \sin (x) \frac{2 \sin (x)}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.2

Multiplica $\sin (x) \frac{2 \sin (x)}{\cos (x)}$ .

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Paso 7.2.1

Combina $\sin (x)$ y $\frac{2 \sin (x)}{\cos (x)}$ .

$\cos (x) + \frac{\sin (x) (2 \sin (x))}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.2.2

Eleva $\sin (x)$ a la potencia de $1$ .

$\cos (x) + \frac{2 (\sin^{1} (x) \sin (x))}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.2.3

Eleva $\sin (x)$ a la potencia de $1$ .

$\cos (x) + \frac{2 (\sin^{1} (x) \sin^{1} (x))}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.2.4

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$\cos (x) + \frac{2 {\sin (x)}^{1 + 1}}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.2.5

Suma $1$ y $1$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.3

Multiplica $\sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)}$ .

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Paso 7.3.1

Combina $\sin (x)$ y $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.3.2

Multiplica $\sin (x)$ por $\sin^{3} (x)$ sumando los exponentes.

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Paso 7.3.2.1

Multiplica $\sin (x)$ por $\sin^{3} (x)$ .

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Paso 7.3.2.1.1

Eleva $\sin (x)$ a la potencia de $1$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{1} (x) \sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.3.2.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 7.3.2.2

Suma $1$ y $3$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

Paso 8

Cancela el factor común de $\sin (x)$ .

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Paso 8.1

Factoriza $\sin (x)$ de $\cos^{3} (x) \sin (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\sin (x) \cos^{3} (x)}$

Paso 8.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\sin (x) \cos^{3} (x)}$

Paso 8.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} = \frac{1}{\cos^{3} (x)}$

Paso 9

Resta $\frac{1}{\cos^{3} (x)}$ de ambos lados de la ecuación.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

Paso 10

Simplifica cada término.

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Paso 10.1

Factoriza $\sin (x)$ de $\sin^{2} (x)$ .

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

Paso 10.2

Separa las fracciones.

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

Paso 10.3

Convierte de $\frac{\sin (x)}{\cos (x)}$ a $\tan (x)$ .

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

Paso 10.4

Divide $2 (\sin (x))$ por $1$ .

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

Paso 10.5

Factoriza $\sin^{3} (x)$ de $\sin^{4} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

Paso 10.6

Multiplica por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = 0$

Paso 10.7

Separa las fracciones.

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

Paso 10.8

Convierte de $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ a $\tan^{3} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

Paso 10.9

Divide $\sin (x)$ por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

Paso 11

Divide cada término en la ecuación por $\cos (x)$ .

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 12

Cancela el factor común de $\cos (x)$ .

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Paso 12.1

Cancela el factor común.

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 12.2

Reescribe la expresión.

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 13

Simplifica el numerador.

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Paso 13.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 13.2

Combina exponentes.

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Paso 13.2.1

Combina $\frac{\sin (x)}{\cos (x)}$ y $2$ .

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 13.2.2

Combina $\frac{\sin (x) \cdot 2}{\cos (x)}$ y $\sin (x)$ .

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 13.2.3

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 13.2.4

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 13.2.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 13.2.6

Suma $1$ y $1$ .

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 14

Multiplica el numerador por la recíproca del denominador.

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 15

Combina fracciones.

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Paso 15.1

Combinar.

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 15.2

Multiplica $2$ por $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 16

Simplifica el denominador.

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Paso 16.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 16.2

Suma $1$ y $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 17

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 18

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 19

Separa las fracciones.

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 20

Convierte de $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ a $\tan^{2} (x)$ .

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 21

Multiplica $2$ por $1$ .

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 22

Divide $2$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 23

Simplifica el numerador.

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Paso 23.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 23.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 24

Combina $\sin (x)$ y $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 25

Multiplica $\sin (x)$ por $\sin^{3} (x)$ sumando los exponentes.

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Paso 25.1

Multiplica $\sin (x)$ por $\sin^{3} (x)$ .

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Paso 25.1.1

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 25.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 25.2

Suma $1$ y $3$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 26

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 27

Combinar.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 28

Multiplica $\cos^{3} (x)$ por $\cos (x)$ sumando los exponentes.

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Paso 28.1

Multiplica $\cos^{3} (x)$ por $\cos (x)$ .

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Paso 28.1.1

Eleva $\cos (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 28.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 28.2

Suma $3$ y $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 29

Multiplica $\sin^{4} (x)$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 30

Convierte de $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ a $\tan^{4} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 31

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 32

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

Paso 33

Combina $\sec (x)$ y $\frac{1}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

Paso 34

Factoriza $\cos (x)$ de $\cos^{3} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

Paso 35

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 36

Reescribe $\sec (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 37

Reescribe $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ como un producto.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

Paso 38

Simplifica.

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Paso 38.1

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

Paso 38.2

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 38.3

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 38.4

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 38.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

Paso 38.6

Suma $1$ y $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 39

Reescribe $1$ como $1^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 40

Reescribe $\frac{1^{2}}{\cos^{2} (x)}$ como ${(\frac{1}{\cos (x)})}^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 41

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 42

Multiplica $\sec^{2} (x)$ por $\sec^{2} (x)$ sumando los exponentes.

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Paso 42.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

Paso 42.2

Suma $2$ y $2$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

Paso 43

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

Paso 44

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

Paso 45

Divide $0$ por $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

Paso 46

Multiplica $0$ por $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 47

Reemplaza $2 \tan^{2} (x)$ con $2 (\sec^{2} (x) - 1)$ según la identidad de $\tan^{2} (x) + 1 = \sec^{2} (x)$ .

$1 + 2 (\sec^{2} (x) - 1) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 48

Simplifica cada término.

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Paso 48.1

Aplica la propiedad distributiva.

$1 + 2 \sec^{2} (x) + 2 \cdot - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 48.2

Multiplica $2$ por $- 1$ .

$1 + 2 \sec^{2} (x) - 2 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 49

Resta $2$ de $1$ .

$2 \sec^{2} (x) - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 50

Reordena el polinomio.

$\tan^{4} (x) - \sec^{4} (x) + 2 \sec^{2} (x) - 1 = 0$

Paso 51

Multiplica ambos lados por $\cos (x)$ .

$(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52

Simplifica.

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Paso 52.1

Simplifica el lado izquierdo.

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Paso 52.1.1

Simplifica $(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x)$ .

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Paso 52.1.1.1

Simplifica cada término.

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Paso 52.1.1.1.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$(1 + 2 {(\frac{\sin (x)}{\cos (x)})}^{2} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.1.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$(1 + 2 \frac{\sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.1.3

Combina $2$ y $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.1.4

Reescribe $\tan (x)$ en términos de senos y cosenos.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + {(\frac{\sin (x)}{\cos (x)})}^{4} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.1.5

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.1.6

Reescribe $\sec (x)$ en términos de senos y cosenos.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - {(\frac{1}{\cos (x)})}^{4}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.1.7

Aplica la regla del producto a $\frac{1}{\cos (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1^{4}}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.1.8

Uno elevado a cualquier potencia es uno.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.2

Aplica la propiedad distributiva.

$1 \cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3

Simplifica.

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Paso 52.1.1.3.1

Multiplica $\cos (x)$ por $1$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.2

Cancela el factor común de $\cos (x)$ .

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Paso 52.1.1.3.2.1

Factoriza $\cos (x)$ de $\cos^{2} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.2.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.2.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.3

Cancela el factor común de $\cos (x)$ .

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Paso 52.1.1.3.3.1

Factoriza $\cos (x)$ de $\cos^{4} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.3.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.3.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.4

Cancela el factor común de $\cos (x)$ .

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Paso 52.1.1.3.4.1

Mueve el signo menos inicial en $- \frac{1}{\cos^{4} (x)}$ al numerador.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.4.2

Factoriza $\cos (x)$ de $\cos^{4} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.4.3

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.3.4.4

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.4

Mueve el negativo al frente de la fracción.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5

Simplifica cada término.

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Paso 52.1.1.5.1

Factoriza $\sin (x)$ de $\sin^{2} (x)$ .

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5.2

Separa las fracciones.

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5.3

Convierte de $\frac{\sin (x)}{\cos (x)}$ a $\tan (x)$ .

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5.4

Divide $2 (\sin (x))$ por $1$ .

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5.5

Factoriza $\sin^{3} (x)$ de $\sin^{4} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5.6

Multiplica por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5.7

Separa las fracciones.

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5.8

Convierte de $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ a $\tan^{3} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.1.1.5.9

Divide $\sin (x)$ por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.2

Simplifica el lado derecho.

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Paso 52.2.1

Cancela el factor común de $\cos (x)$ .

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Paso 52.2.1.1

Cancela el factor común.

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 52.2.1.2

Reescribe la expresión.

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

Paso 53

Resuelve $x$

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Paso 53.1

Divide cada término en la ecuación por $\cos (x)$ .

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.2

Cancela el factor común de $\cos (x)$ .

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Paso 53.2.1

Cancela el factor común.

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.2.2

Reescribe la expresión.

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.3

Simplifica el numerador.

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Paso 53.3.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.3.2

Combina exponentes.

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Paso 53.3.2.1

Combina $\frac{\sin (x)}{\cos (x)}$ y $2$ .

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.3.2.2

Combina $\frac{\sin (x) \cdot 2}{\cos (x)}$ y $\sin (x)$ .

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.3.2.3

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.3.2.4

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.3.2.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.3.2.6

Suma $1$ y $1$ .

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.4

Multiplica el numerador por la recíproca del denominador.

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.5

Combina fracciones.

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Paso 53.5.1

Combinar.

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.5.2

Multiplica $2$ por $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.6

Simplifica el denominador.

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Paso 53.6.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.6.2

Suma $1$ y $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.7

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.8

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.9

Separa las fracciones.

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.10

Convierte de $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ a $\tan^{2} (x)$ .

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.11

Multiplica $2$ por $1$ .

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.12

Divide $2$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.13

Simplifica el numerador.

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Paso 53.13.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.13.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.14

Combina $\sin (x)$ y $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.15

Multiplica $\sin (x)$ por $\sin^{3} (x)$ sumando los exponentes.

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Paso 53.15.1

Multiplica $\sin (x)$ por $\sin^{3} (x)$ .

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Paso 53.15.1.1

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.15.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.15.2

Suma $1$ y $3$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.16

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.17

Combinar.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.18

Multiplica $\cos^{3} (x)$ por $\cos (x)$ sumando los exponentes.

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Paso 53.18.1

Multiplica $\cos^{3} (x)$ por $\cos (x)$ .

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Paso 53.18.1.1

Eleva $\cos (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.18.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.18.2

Suma $3$ y $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.19

Multiplica $\sin^{4} (x)$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.20

Convierte de $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ a $\tan^{4} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.21

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.22

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

Paso 53.23

Combina $\sec (x)$ y $\frac{1}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

Paso 53.24

Factoriza $\cos (x)$ de $\cos^{3} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

Paso 53.25

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 53.26

Reescribe $\sec (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 53.27

Reescribe $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ como un producto.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

Paso 53.28

Simplifica.

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Paso 53.28.1

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

Paso 53.28.2

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.28.3

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.28.4

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.28.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

Paso 53.28.6

Suma $1$ y $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.29

Reescribe $1$ como $1^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.30

Reescribe $\frac{1^{2}}{\cos^{2} (x)}$ como ${(\frac{1}{\cos (x)})}^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.31

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.32

Multiplica $\sec^{2} (x)$ por $\sec^{2} (x)$ sumando los exponentes.

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Paso 53.32.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

Paso 53.32.2

Suma $2$ y $2$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

Paso 53.33

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

Paso 53.34

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

Paso 53.35

Divide $0$ por $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

Paso 53.36

Multiplica $0$ por $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.37

Reemplaza $2 \tan^{2} (x)$ con $2 (\sec^{2} (x) - 1)$ según la identidad de $\tan^{2} (x) + 1 = \sec^{2} (x)$ .

$1 + 2 (\sec^{2} (x) - 1) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.38

Simplifica cada término.

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Paso 53.38.1

Aplica la propiedad distributiva.

$1 + 2 \sec^{2} (x) + 2 \cdot - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.38.2

Multiplica $2$ por $- 1$ .

$1 + 2 \sec^{2} (x) - 2 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.39

Resta $2$ de $1$ .

$2 \sec^{2} (x) - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.40

Reordena el polinomio.

$\tan^{4} (x) - \sec^{4} (x) + 2 \sec^{2} (x) - 1 = 0$

Paso 53.41

Multiplica ambos lados por $\cos (x)$ .

$(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42

Simplifica.

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Paso 53.42.1

Simplifica el lado izquierdo.

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Paso 53.42.1.1

Simplifica $(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x)$ .

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Paso 53.42.1.1.1

Simplifica cada término.

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Paso 53.42.1.1.1.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$(1 + 2 {(\frac{\sin (x)}{\cos (x)})}^{2} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.1.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$(1 + 2 \frac{\sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.1.3

Combina $2$ y $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.1.4

Reescribe $\tan (x)$ en términos de senos y cosenos.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + {(\frac{\sin (x)}{\cos (x)})}^{4} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.1.5

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.1.6

Reescribe $\sec (x)$ en términos de senos y cosenos.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - {(\frac{1}{\cos (x)})}^{4}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.1.7

Aplica la regla del producto a $\frac{1}{\cos (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1^{4}}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.1.8

Uno elevado a cualquier potencia es uno.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.2

Aplica la propiedad distributiva.

$1 \cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3

Simplifica.

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Paso 53.42.1.1.3.1

Multiplica $\cos (x)$ por $1$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.2

Cancela el factor común de $\cos (x)$ .

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Paso 53.42.1.1.3.2.1

Factoriza $\cos (x)$ de $\cos^{2} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.2.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.2.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.3

Cancela el factor común de $\cos (x)$ .

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Paso 53.42.1.1.3.3.1

Factoriza $\cos (x)$ de $\cos^{4} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.3.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.3.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.4

Cancela el factor común de $\cos (x)$ .

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Paso 53.42.1.1.3.4.1

Mueve el signo menos inicial en $- \frac{1}{\cos^{4} (x)}$ al numerador.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.4.2

Factoriza $\cos (x)$ de $\cos^{4} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.4.3

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.3.4.4

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.4

Mueve el negativo al frente de la fracción.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5

Simplifica cada término.

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Paso 53.42.1.1.5.1

Factoriza $\sin (x)$ de $\sin^{2} (x)$ .

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5.2

Separa las fracciones.

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5.3

Convierte de $\frac{\sin (x)}{\cos (x)}$ a $\tan (x)$ .

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5.4

Divide $2 (\sin (x))$ por $1$ .

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5.5

Factoriza $\sin^{3} (x)$ de $\sin^{4} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5.6

Multiplica por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5.7

Separa las fracciones.

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5.8

Convierte de $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ a $\tan^{3} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.1.1.5.9

Divide $\sin (x)$ por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.2

Simplifica el lado derecho.

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Paso 53.42.2.1

Cancela el factor común de $\cos (x)$ .

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Paso 53.42.2.1.1

Cancela el factor común.

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.42.2.1.2

Reescribe la expresión.

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

Paso 53.43

Resuelve $x$

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Paso 53.43.1

Divide cada término en la ecuación por $\cos (x)$ .

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.2

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.2.1

Cancela el factor común.

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.2.2

Reescribe la expresión.

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.3

Simplifica el numerador.

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Paso 53.43.3.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.3.2

Combina exponentes.

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Paso 53.43.3.2.1

Combina $\frac{\sin (x)}{\cos (x)}$ y $2$ .

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.3.2.2

Combina $\frac{\sin (x) \cdot 2}{\cos (x)}$ y $\sin (x)$ .

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.3.2.3

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.3.2.4

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.3.2.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.3.2.6

Suma $1$ y $1$ .

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.4

Multiplica el numerador por la recíproca del denominador.

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.5

Combina fracciones.

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Paso 53.43.5.1

Combinar.

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.5.2

Multiplica $2$ por $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.6

Simplifica el denominador.

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Paso 53.43.6.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.6.2

Suma $1$ y $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.7

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.8

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.9

Separa las fracciones.

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.10

Convierte de $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ a $\tan^{2} (x)$ .

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.11

Multiplica $2$ por $1$ .

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.12

Divide $2$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.13

Simplifica el numerador.

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Paso 53.43.13.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.13.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.14

Combina $\sin (x)$ y $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.15

Multiplica $\sin (x)$ por $\sin^{3} (x)$ sumando los exponentes.

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Paso 53.43.15.1

Multiplica $\sin (x)$ por $\sin^{3} (x)$ .

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Paso 53.43.15.1.1

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.15.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.15.2

Suma $1$ y $3$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.16

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.17

Combinar.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.18

Multiplica $\cos^{3} (x)$ por $\cos (x)$ sumando los exponentes.

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Paso 53.43.18.1

Multiplica $\cos^{3} (x)$ por $\cos (x)$ .

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Paso 53.43.18.1.1

Eleva $\cos (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.18.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.18.2

Suma $3$ y $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.19

Multiplica $\sin^{4} (x)$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.20

Convierte de $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ a $\tan^{4} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.21

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.22

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

Paso 53.43.23

Combina $\sec (x)$ y $\frac{1}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

Paso 53.43.24

Factoriza $\cos (x)$ de $\cos^{3} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

Paso 53.43.25

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 53.43.26

Reescribe $\sec (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 53.43.27

Reescribe $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ como un producto.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

Paso 53.43.28

Simplifica.

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Paso 53.43.28.1

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

Paso 53.43.28.2

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.28.3

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.28.4

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.28.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

Paso 53.43.28.6

Suma $1$ y $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.29

Reescribe $1$ como $1^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.30

Reescribe $\frac{1^{2}}{\cos^{2} (x)}$ como ${(\frac{1}{\cos (x)})}^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.31

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.32

Multiplica $\sec^{2} (x)$ por $\sec^{2} (x)$ sumando los exponentes.

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Paso 53.43.32.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

Paso 53.43.32.2

Suma $2$ y $2$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

Paso 53.43.33

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

Paso 53.43.34

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

Paso 53.43.35

Divide $0$ por $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

Paso 53.43.36

Multiplica $0$ por $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.37

Reemplaza $2 \tan^{2} (x)$ con $2 (\sec^{2} (x) - 1)$ según la identidad de $\tan^{2} (x) + 1 = \sec^{2} (x)$ .

$1 + 2 (\sec^{2} (x) - 1) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.38

Simplifica cada término.

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Paso 53.43.38.1

Aplica la propiedad distributiva.

$1 + 2 \sec^{2} (x) + 2 \cdot - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.38.2

Multiplica $2$ por $- 1$ .

$1 + 2 \sec^{2} (x) - 2 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.39

Resta $2$ de $1$ .

$2 \sec^{2} (x) - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.40

Reordena el polinomio.

$\tan^{4} (x) - \sec^{4} (x) + 2 \sec^{2} (x) - 1 = 0$

Paso 53.43.41

Multiplica ambos lados por $\cos (x)$ .

$(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42

Simplifica.

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Paso 53.43.42.1

Simplifica el lado izquierdo.

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Paso 53.43.42.1.1

Simplifica $(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x)$ .

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Paso 53.43.42.1.1.1

Simplifica cada término.

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Paso 53.43.42.1.1.1.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$(1 + 2 {(\frac{\sin (x)}{\cos (x)})}^{2} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.1.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$(1 + 2 \frac{\sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.1.3

Combina $2$ y $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.1.4

Reescribe $\tan (x)$ en términos de senos y cosenos.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + {(\frac{\sin (x)}{\cos (x)})}^{4} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.1.5

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.1.6

Reescribe $\sec (x)$ en términos de senos y cosenos.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - {(\frac{1}{\cos (x)})}^{4}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.1.7

Aplica la regla del producto a $\frac{1}{\cos (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1^{4}}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.1.8

Uno elevado a cualquier potencia es uno.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.2

Aplica la propiedad distributiva.

$1 \cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3

Simplifica.

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Paso 53.43.42.1.1.3.1

Multiplica $\cos (x)$ por $1$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.2

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.42.1.1.3.2.1

Factoriza $\cos (x)$ de $\cos^{2} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.2.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.2.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.3

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.42.1.1.3.3.1

Factoriza $\cos (x)$ de $\cos^{4} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.3.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.3.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.4

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.42.1.1.3.4.1

Mueve el signo menos inicial en $- \frac{1}{\cos^{4} (x)}$ al numerador.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.4.2

Factoriza $\cos (x)$ de $\cos^{4} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.4.3

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.3.4.4

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.4

Mueve el negativo al frente de la fracción.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5

Simplifica cada término.

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Paso 53.43.42.1.1.5.1

Factoriza $\sin (x)$ de $\sin^{2} (x)$ .

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5.2

Separa las fracciones.

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5.3

Convierte de $\frac{\sin (x)}{\cos (x)}$ a $\tan (x)$ .

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5.4

Divide $2 (\sin (x))$ por $1$ .

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5.5

Factoriza $\sin^{3} (x)$ de $\sin^{4} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5.6

Multiplica por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5.7

Separa las fracciones.

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5.8

Convierte de $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ a $\tan^{3} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.1.1.5.9

Divide $\sin (x)$ por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.2

Simplifica el lado derecho.

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Paso 53.43.42.2.1

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.42.2.1.1

Cancela el factor común.

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.42.2.1.2

Reescribe la expresión.

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

Paso 53.43.43

Resuelve $x$

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Paso 53.43.43.1

Divide cada término en la ecuación por $\cos (x)$ .

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.2

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.43.2.1

Cancela el factor común.

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.2.2

Reescribe la expresión.

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.3

Simplifica el numerador.

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Paso 53.43.43.3.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.3.2

Combina exponentes.

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Paso 53.43.43.3.2.1

Combina $\frac{\sin (x)}{\cos (x)}$ y $2$ .

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.3.2.2

Combina $\frac{\sin (x) \cdot 2}{\cos (x)}$ y $\sin (x)$ .

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.3.2.3

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.3.2.4

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.3.2.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.3.2.6

Suma $1$ y $1$ .

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.4

Multiplica el numerador por la recíproca del denominador.

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.5

Combina fracciones.

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Paso 53.43.43.5.1

Combinar.

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.5.2

Multiplica $2$ por $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.6

Simplifica el denominador.

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Paso 53.43.43.6.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.6.2

Suma $1$ y $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.7

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.8

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.9

Separa las fracciones.

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.10

Convierte de $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ a $\tan^{2} (x)$ .

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.11

Multiplica $2$ por $1$ .

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.12

Divide $2$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.13

Simplifica el numerador.

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Paso 53.43.43.13.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.13.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.14

Combina $\sin (x)$ y $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.15

Multiplica $\sin (x)$ por $\sin^{3} (x)$ sumando los exponentes.

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Paso 53.43.43.15.1

Multiplica $\sin (x)$ por $\sin^{3} (x)$ .

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Paso 53.43.43.15.1.1

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.15.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.15.2

Suma $1$ y $3$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.16

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.17

Combinar.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.18

Multiplica $\cos^{3} (x)$ por $\cos (x)$ sumando los exponentes.

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Paso 53.43.43.18.1

Multiplica $\cos^{3} (x)$ por $\cos (x)$ .

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Paso 53.43.43.18.1.1

Eleva $\cos (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.18.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.18.2

Suma $3$ y $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.19

Multiplica $\sin^{4} (x)$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.20

Convierte de $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ a $\tan^{4} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.21

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.22

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

Paso 53.43.43.23

Combina $\sec (x)$ y $\frac{1}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.24

Factoriza $\cos (x)$ de $\cos^{3} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.25

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 53.43.43.26

Reescribe $\sec (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 53.43.43.27

Reescribe $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ como un producto.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

Paso 53.43.43.28

Simplifica.

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Paso 53.43.43.28.1

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

Paso 53.43.43.28.2

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.43.28.3

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.43.28.4

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.43.28.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

Paso 53.43.43.28.6

Suma $1$ y $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.43.29

Reescribe $1$ como $1^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.43.30

Reescribe $\frac{1^{2}}{\cos^{2} (x)}$ como ${(\frac{1}{\cos (x)})}^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.43.31

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.43.32

Multiplica $\sec^{2} (x)$ por $\sec^{2} (x)$ sumando los exponentes.

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Paso 53.43.43.32.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

Paso 53.43.43.32.2

Suma $2$ y $2$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

Paso 53.43.43.33

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

Paso 53.43.43.34

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

Paso 53.43.43.35

Divide $0$ por $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

Paso 53.43.43.36

Multiplica $0$ por $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.43.37

Reemplaza $2 \tan^{2} (x)$ con $2 (\sec^{2} (x) - 1)$ según la identidad de $\tan^{2} (x) + 1 = \sec^{2} (x)$ .

$1 + 2 (\sec^{2} (x) - 1) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.43.38

Simplifica cada término.

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Paso 53.43.43.38.1

Aplica la propiedad distributiva.

$1 + 2 \sec^{2} (x) + 2 \cdot - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.43.38.2

Multiplica $2$ por $- 1$ .

$1 + 2 \sec^{2} (x) - 2 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.43.39

Resta $2$ de $1$ .

$2 \sec^{2} (x) - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.43.40

Reordena el polinomio.

$\tan^{4} (x) - \sec^{4} (x) + 2 \sec^{2} (x) - 1 = 0$

Paso 53.43.43.41

Multiplica ambos lados por $\cos (x)$ .

$(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42

Simplifica.

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Paso 53.43.43.42.1

Simplifica el lado izquierdo.

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Paso 53.43.43.42.1.1

Simplifica $(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x)$ .

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Paso 53.43.43.42.1.1.1

Simplifica cada término.

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Paso 53.43.43.42.1.1.1.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$(1 + 2 {(\frac{\sin (x)}{\cos (x)})}^{2} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.1.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$(1 + 2 \frac{\sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.1.3

Combina $2$ y $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.1.4

Reescribe $\tan (x)$ en términos de senos y cosenos.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + {(\frac{\sin (x)}{\cos (x)})}^{4} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.1.5

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.1.6

Reescribe $\sec (x)$ en términos de senos y cosenos.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - {(\frac{1}{\cos (x)})}^{4}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.1.7

Aplica la regla del producto a $\frac{1}{\cos (x)}$ .

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1^{4}}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.1.8

Uno elevado a cualquier potencia es uno.

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.2

Aplica la propiedad distributiva.

$1 \cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3

Simplifica.

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Paso 53.43.43.42.1.1.3.1

Multiplica $\cos (x)$ por $1$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.2

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.43.42.1.1.3.2.1

Factoriza $\cos (x)$ de $\cos^{2} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.2.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.2.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.3

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.43.42.1.1.3.3.1

Factoriza $\cos (x)$ de $\cos^{4} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.3.2

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.3.3

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.4

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.43.42.1.1.3.4.1

Mueve el signo menos inicial en $- \frac{1}{\cos^{4} (x)}$ al numerador.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.4.2

Factoriza $\cos (x)$ de $\cos^{4} (x)$ .

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.4.3

Cancela el factor común.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.3.4.4

Reescribe la expresión.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.4

Mueve el negativo al frente de la fracción.

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5

Simplifica cada término.

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Paso 53.43.43.42.1.1.5.1

Factoriza $\sin (x)$ de $\sin^{2} (x)$ .

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5.2

Separa las fracciones.

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5.3

Convierte de $\frac{\sin (x)}{\cos (x)}$ a $\tan (x)$ .

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5.4

Divide $2 (\sin (x))$ por $1$ .

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5.5

Factoriza $\sin^{3} (x)$ de $\sin^{4} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5.6

Multiplica por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5.7

Separa las fracciones.

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5.8

Convierte de $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ a $\tan^{3} (x)$ .

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.1.1.5.9

Divide $\sin (x)$ por $1$ .

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.2

Simplifica el lado derecho.

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Paso 53.43.43.42.2.1

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.43.42.2.1.1

Cancela el factor común.

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

Paso 53.43.43.42.2.1.2

Reescribe la expresión.

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

Paso 53.43.43.43

Resuelve $x$

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Paso 53.43.43.43.1

Divide cada término en la ecuación por $\cos (x)$ .

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.2

Cancela el factor común de $\cos (x)$ .

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Paso 53.43.43.43.2.1

Cancela el factor común.

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.2.2

Reescribe la expresión.

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.3

Simplifica el numerador.

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Paso 53.43.43.43.3.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.3.2

Combina exponentes.

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Paso 53.43.43.43.3.2.1

Combina $\frac{\sin (x)}{\cos (x)}$ y $2$ .

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.3.2.2

Combina $\frac{\sin (x) \cdot 2}{\cos (x)}$ y $\sin (x)$ .

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.3.2.3

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.3.2.4

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.3.2.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.3.2.6

Suma $1$ y $1$ .

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.4

Multiplica el numerador por la recíproca del denominador.

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.5

Combina fracciones.

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Paso 53.43.43.43.5.1

Combinar.

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.5.2

Multiplica $2$ por $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.6

Simplifica el denominador.

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Paso 53.43.43.43.6.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.6.2

Suma $1$ y $1$ .

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.7

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.8

Multiplica por $1$ .

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.9

Separa las fracciones.

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.10

Convierte de $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ a $\tan^{2} (x)$ .

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.11

Multiplica $2$ por $1$ .

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.12

Divide $2$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.13

Simplifica el numerador.

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Paso 53.43.43.43.13.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.13.2

Aplica la regla del producto a $\frac{\sin (x)}{\cos (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.14

Combina $\sin (x)$ y $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.15

Multiplica $\sin (x)$ por $\sin^{3} (x)$ sumando los exponentes.

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Paso 53.43.43.43.15.1

Multiplica $\sin (x)$ por $\sin^{3} (x)$ .

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Paso 53.43.43.43.15.1.1

Eleva $\sin (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.15.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.15.2

Suma $1$ y $3$ .

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.16

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.17

Combinar.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.18

Multiplica $\cos^{3} (x)$ por $\cos (x)$ sumando los exponentes.

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Paso 53.43.43.43.18.1

Multiplica $\cos^{3} (x)$ por $\cos (x)$ .

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Paso 53.43.43.43.18.1.1

Eleva $\cos (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.18.1.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.18.2

Suma $3$ y $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.19

Multiplica $\sin^{4} (x)$ por $1$ .

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.20

Convierte de $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ a $\tan^{4} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.21

Multiplica el numerador por la recíproca del denominador.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.22

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.23

Combina $\sec (x)$ y $\frac{1}{\cos^{3} (x)}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.24

Factoriza $\cos (x)$ de $\cos^{3} (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.25

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.26

Reescribe $\sec (x)$ en términos de senos y cosenos.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.27

Reescribe $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ como un producto.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.28

Simplifica.

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Paso 53.43.43.43.28.1

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.28.2

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.28.3

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.28.4

Eleva $\sec (x)$ a la potencia de $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.28.5

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.28.6

Suma $1$ y $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.29

Reescribe $1$ como $1^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.30

Reescribe $\frac{1^{2}}{\cos^{2} (x)}$ como ${(\frac{1}{\cos (x)})}^{2}$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.31

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.32

Multiplica $\sec^{2} (x)$ por $\sec^{2} (x)$ sumando los exponentes.

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Paso 53.43.43.43.32.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

Paso 53.43.43.43.32.2

Suma $2$ y $2$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

Paso 53.43.43.43.33

Separa las fracciones.

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

Paso 53.43.43.43.34

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

Paso 53.43.43.43.35

Divide $0$ por $1$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

Paso 53.43.43.43.36

Multiplica $0$ por $\sec (x)$ .

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.43.43.37

Simplifica el lado izquierdo.

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Paso 53.43.43.43.37.1

Simplifica $1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)$ .

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Paso 53.43.43.43.37.1.1

Factoriza con la regla del cuadrado perfecto.

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Paso 53.43.43.43.37.1.1.1

Reescribe $1$ como $1^{2}$ .

$1^{2} + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

Paso 53.43.43.43.37.1.1.2

Reescribe $\tan^{4} (x)$ como ${(\tan^{2} (x))}^{2}$ .

$1^{2} + 2 \tan^{2} (x) + {(\tan^{2} (x))}^{2} - \sec^{4} (x) = 0$

Paso 53.43.43.43.37.1.1.3

Comprueba que el término medio sea dos veces el producto de los números que se elevan al cuadrado en el primer término y el tercer término.

$2 \tan^{2} (x) = 2 \cdot 1 \cdot \tan^{2} (x)$

Paso 53.43.43.43.37.1.1.4

Reescribe el polinomio.

$1^{2} + 2 \cdot 1 \cdot \tan^{2} (x) + {(\tan^{2} (x))}^{2} - \sec^{4} (x) = 0$

Paso 53.43.43.43.37.1.1.5

Factoriza con la regla del trinomio cuadrado perfecto $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , donde $a = 1$ y $b = \tan^{2} (x)$ .

${(1 + \tan^{2} (x))}^{2} - \sec^{4} (x) = 0$

Paso 53.43.43.43.37.1.2

Reescribe $\sec^{4} (x)$ como ${(\sec^{2} (x))}^{2}$ .

${(1 + \tan^{2} (x))}^{2} - {(\sec^{2} (x))}^{2} = 0$

Paso 53.43.43.43.37.1.3

Dado que ambos términos son cuadrados perfectos, factoriza con la fórmula de la diferencia de cuadrados, $a^{2} - b^{2} = (a + b) (a - b)$ , donde $a = 1 + \tan^{2} (x)$ y $b = \sec^{2} (x)$ .

$(1 + \tan^{2} (x) + \sec^{2} (x)) (1 + \tan^{2} (x) - \sec^{2} (x)) = 0$

Paso 53.43.43.43.37.1.4

Reorganiza los términos.

$(\tan^{2} (x) + 1 + \sec^{2} (x)) (1 + \tan^{2} (x) - \sec^{2} (x)) = 0$

Paso 53.43.43.43.37.1.5

Aplica la identidad pitagórica.

$(\sec^{2} (x) + \sec^{2} (x)) (1 + \tan^{2} (x) - \sec^{2} (x)) = 0$

Paso 53.43.43.43.37.1.6

Suma $\sec^{2} (x)$ y $\sec^{2} (x)$ .

$2 \sec^{2} (x) (1 + \tan^{2} (x) - \sec^{2} (x)) = 0$

Paso 53.43.43.43.37.1.7

Reorganiza los términos.

$2 \sec^{2} (x) (\tan^{2} (x) + 1 - \sec^{2} (x)) = 0$

Paso 53.43.43.43.37.1.8

Aplica la identidad pitagórica.

$2 \sec^{2} (x) (\sec^{2} (x) - \sec^{2} (x)) = 0$

Paso 53.43.43.43.37.1.9

Resta $\sec^{2} (x)$ de $\sec^{2} (x)$ .

$2 \sec^{2} (x) \cdot 0 = 0$

Paso 53.43.43.43.37.1.10

Multiplica $2 \sec^{2} (x) \cdot 0$ .

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Paso 53.43.43.43.37.1.10.1

Multiplica $0$ por $2$ .

$0 \sec^{2} (x) = 0$

Paso 53.43.43.43.37.1.10.2

Multiplica $0$ por $\sec^{2} (x)$ .

$0 = 0$

Paso 53.43.43.43.38

Como $0 = 0$ , la ecuación siempre será verdadera para cualquier valor de $x$ .

Todos los números reales

Paso 54

El resultado puede mostrarse de distintas formas.

Todos los números reales

Notación de intervalo:

$(- \infty, \infty)$