Trigonometría Ejemplos

$\frac{\tan (x) \sin (x)}{\tan (x) + \sin (x)}$

Step 1

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

$\frac{\frac{\sin (x)}{\cos (x)} \sin (x)}{\tan (x) + \sin (x)}$

Step 2

Simplifica el denominador.

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

$\frac{\frac{\sin (x)}{\cos (x)} \sin (x)}{\frac{\sin (x)}{\cos (x)} + \sin (x)}$

Factoriza $\sin (x)$ de $\frac{\sin (x)}{\cos (x)} + \sin (x)$ .

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

$\frac{\frac{\sin (x)}{\cos (x)} \sin (x)}{\sin (x) \frac{1}{\cos (x)} + \sin (x)}$

Multiplica por $1$ .

$\frac{\frac{\sin (x)}{\cos (x)} \sin (x)}{\sin (x) \frac{1}{\cos (x)} + \sin (x) \cdot 1}$

Factoriza $\sin (x)$ de $\sin (x) \frac{1}{\cos (x)} + \sin (x) \cdot 1$ .

$\frac{\frac{\sin (x)}{\cos (x)} \sin (x)}{\sin (x) (\frac{1}{\cos (x)} + 1)}$

Step 3

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

$\frac{\frac{\sin (x) \sin (x)}{\cos (x)}}{\sin (x) (\frac{1}{\cos (x)} + 1)}$

Step 4

Simplifica el numerador.

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

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

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

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

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

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

Suma $1$ y $1$ .

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

Step 5

Multiplica el numerador por la recíproca del denominador.

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

Step 6

Combinar.

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

Step 7

Cancela el factor común de $\sin^{2} (x)$ y $\sin (x)$ .

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Factoriza $\sin (x)$ de $\sin^{2} (x) \cdot 1$ .

$\frac{\sin (x) (\sin (x) \cdot 1)}{\cos (x) (\sin (x) (\frac{1}{\cos (x)} + 1))}$

Cancela los factores comunes.

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Factoriza $\sin (x)$ de $\cos (x) (\sin (x) (\frac{1}{\cos (x)} + 1))$ .

$\frac{\sin (x) (\sin (x) \cdot 1)}{\sin (x) (\cos (x) (\frac{1}{\cos (x)} + 1))}$

Cancela el factor común.

$\frac{\sin (x) (\sin (x) \cdot 1)}{\sin (x) (\cos (x) (\frac{1}{\cos (x)} + 1))}$

Reescribe la expresión.

$\frac{\sin (x) \cdot 1}{\cos (x) (\frac{1}{\cos (x)} + 1)}$

Step 8

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

$\frac{\sin (x)}{\cos (x) (\frac{1}{\cos (x)} + 1)}$

Step 9

Separa las fracciones.

$\frac{1}{\frac{1}{\cos (x)} + 1} \cdot \frac{\sin (x)}{\cos (x)}$

Step 10

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

$\frac{1}{\frac{1}{\cos (x)} + 1} \tan (x)$

Step 11

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

$\frac{1}{\sec (x) + 1} \tan (x)$

Step 12

Combina $\frac{1}{\sec (x) + 1}$ y $\tan (x)$ .

$\frac{\tan (x)}{\sec (x) + 1}$