Trigonometría Ejemplos

${(- 4 \cos (x) \sin (x) + 2 \cos (2 x))}^{2} + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Step 1

Simplifica cada término.

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Reescribe ${(- 4 \cos (x) \sin (x) + 2 \cos (2 x))}^{2}$ como $(- 4 \cos (x) \sin (x) + 2 \cos (2 x)) (- 4 \cos (x) \sin (x) + 2 \cos (2 x))$ .

$(- 4 \cos (x) \sin (x) + 2 \cos (2 x)) (- 4 \cos (x) \sin (x) + 2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Expande $(- 4 \cos (x) \sin (x) + 2 \cos (2 x)) (- 4 \cos (x) \sin (x) + 2 \cos (2 x))$ con el método PEIU (primero, exterior, interior, ultimo).

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Aplica la propiedad distributiva.

$- 4 \cos (x) \sin (x) (- 4 \cos (x) \sin (x) + 2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x) + 2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Aplica la propiedad distributiva.

$- 4 \cos (x) \sin (x) (- 4 \cos (x) \sin (x)) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x) + 2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Aplica la propiedad distributiva.

$- 4 \cos (x) \sin (x) (- 4 \cos (x) \sin (x)) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Simplifica y combina los términos similares.

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Simplifica cada término.

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Multiplica $- 4 \cos (x) \sin (x) (- 4 \cos (x) \sin (x))$ .

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Multiplica $- 4$ por $- 4$ .

$16 \cos (x) \sin (x) (\cos (x) \sin (x)) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

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

$16 (\cos^{1} (x) \cos (x)) \sin (x) \sin (x) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

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

$16 (\cos^{1} (x) \cos^{1} (x)) \sin (x) \sin (x) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

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

$16 {\cos (x)}^{1 + 1} \sin (x) \sin (x) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Suma $1$ y $1$ .

$16 \cos^{2} (x) \sin (x) \sin (x) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

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

$16 \cos^{2} (x) (\sin^{1} (x) \sin (x)) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

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

$16 \cos^{2} (x) (\sin^{1} (x) \sin^{1} (x)) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

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

$16 \cos^{2} (x) {\sin (x)}^{1 + 1} - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Suma $1$ y $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Agrega paréntesis.

$16 \cos^{2} (x) \sin^{2} (x) - 4 \cos (x) (\sin (x) \cdot 2) \cos (2 x) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Agrega paréntesis.

$16 \cos^{2} (x) \sin^{2} (x) - 4 (\cos (x) (\sin (x) \cdot 2)) \cos (2 x) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Reordena $\cos (x)$ y $\sin (x) \cdot 2$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 (\sin (x) \cdot 2 \cos (x)) \cos (2 x) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Reordena $\sin (x)$ y $2$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 (2 \cdot \sin (x) \cos (x)) \cos (2 x) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Aplica la razón del ángulo doble sinusoidal.

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) + 2 \cos (2 x) (- 4 \cos (x) \sin (x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Reordena $2 \cos (2 x)$ y $- 4 \cos (x) \sin (x)$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 \cos (x) \sin (x) (2 \cos (2 x)) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Agrega paréntesis.

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 \cos (x) (\sin (x) \cdot 2) \cos (2 x) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Agrega paréntesis.

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 (\cos (x) (\sin (x) \cdot 2)) \cos (2 x) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Reordena $\cos (x)$ y $\sin (x) \cdot 2$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 (\sin (x) \cdot 2 \cos (x)) \cos (2 x) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Reordena $\sin (x)$ y $2$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 (2 \cdot \sin (x) \cos (x)) \cos (2 x) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Aplica la razón del ángulo doble sinusoidal.

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 \sin (2 x) \cos (2 x) + 2 \cos (2 x) (2 \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Multiplica $2 \cos (2 x) (2 \cos (2 x))$ .

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Multiplica $2$ por $2$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 \sin (2 x) \cos (2 x) + 4 \cos (2 x) \cos (2 x) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Eleva $\cos (2 x)$ a la potencia de $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 \sin (2 x) \cos (2 x) + 4 (\cos^{1} (2 x) \cos (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Eleva $\cos (2 x)$ a la potencia de $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 \sin (2 x) \cos (2 x) + 4 (\cos^{1} (2 x) \cos^{1} (2 x)) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

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

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 \sin (2 x) \cos (2 x) + 4 {\cos (2 x)}^{1 + 1} + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Suma $1$ y $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 4 \sin (2 x) \cos (2 x) - 4 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Resta $4 \sin (2 x) \cos (2 x)$ de $- 4 \sin (2 x) \cos (2 x)$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + {(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$

Reescribe ${(2 \cos (2 x) + 4 \sin (x) \cos (x))}^{2}$ como $(2 \cos (2 x) + 4 \sin (x) \cos (x)) (2 \cos (2 x) + 4 \sin (x) \cos (x))$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + (2 \cos (2 x) + 4 \sin (x) \cos (x)) (2 \cos (2 x) + 4 \sin (x) \cos (x))$

Expande $(2 \cos (2 x) + 4 \sin (x) \cos (x)) (2 \cos (2 x) + 4 \sin (x) \cos (x))$ con el método PEIU (primero, exterior, interior, ultimo).

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Aplica la propiedad distributiva.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 2 \cos (2 x) (2 \cos (2 x) + 4 \sin (x) \cos (x)) + 4 \sin (x) \cos (x) (2 \cos (2 x) + 4 \sin (x) \cos (x))$

Aplica la propiedad distributiva.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 2 \cos (2 x) (2 \cos (2 x)) + 2 \cos (2 x) (4 \sin (x) \cos (x)) + 4 \sin (x) \cos (x) (2 \cos (2 x) + 4 \sin (x) \cos (x))$

Aplica la propiedad distributiva.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 2 \cos (2 x) (2 \cos (2 x)) + 2 \cos (2 x) (4 \sin (x) \cos (x)) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Simplifica y combina los términos similares.

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Simplifica cada término.

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Multiplica $2 \cos (2 x) (2 \cos (2 x))$ .

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Multiplica $2$ por $2$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos (2 x) \cos (2 x) + 2 \cos (2 x) (4 \sin (x) \cos (x)) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Eleva $\cos (2 x)$ a la potencia de $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 (\cos^{1} (2 x) \cos (2 x)) + 2 \cos (2 x) (4 \sin (x) \cos (x)) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Eleva $\cos (2 x)$ a la potencia de $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 (\cos^{1} (2 x) \cos^{1} (2 x)) + 2 \cos (2 x) (4 \sin (x) \cos (x)) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

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

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 {\cos (2 x)}^{1 + 1} + 2 \cos (2 x) (4 \sin (x) \cos (x)) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Suma $1$ y $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 2 \cos (2 x) (4 \sin (x) \cos (x)) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Reordena $2 \cos (2 x)$ y $4 \sin (x) \cos (x)$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Agrega paréntesis.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (x) (\cos (x) \cdot 2) \cos (2 x) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Agrega paréntesis.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 (\sin (x) (\cos (x) \cdot 2)) \cos (2 x) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Reordena $\sin (x) \cos (x)$ y $2$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 (2 \cdot (\sin (x) \cos (x))) \cos (2 x) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Aplica la razón del ángulo doble sinusoidal.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (x) \cos (x) (2 \cos (2 x)) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Agrega paréntesis.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (x) (\cos (x) \cdot 2) \cos (2 x) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Agrega paréntesis.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 (\sin (x) (\cos (x) \cdot 2)) \cos (2 x) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Reordena $\sin (x) \cos (x)$ y $2$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 (2 \cdot (\sin (x) \cos (x))) \cos (2 x) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Aplica la razón del ángulo doble sinusoidal.

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$

Multiplica $4 \sin (x) \cos (x) (4 \sin (x) \cos (x))$ .

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Multiplica $4$ por $4$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 \sin (x) \cos (x) (\sin (x) \cos (x))$

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

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 (\sin^{1} (x) \sin (x)) \cos (x) \cos (x)$

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

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 (\sin^{1} (x) \sin^{1} (x)) \cos (x) \cos (x)$

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

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 {\sin (x)}^{1 + 1} \cos (x) \cos (x)$

Suma $1$ y $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 \sin^{2} (x) \cos (x) \cos (x)$

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

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 \sin^{2} (x) (\cos^{1} (x) \cos (x))$

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

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 \sin^{2} (x) (\cos^{1} (x) \cos^{1} (x))$

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

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 \sin^{2} (x) {\cos (x)}^{1 + 1}$

Suma $1$ y $1$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 4 \sin (2 x) \cos (2 x) + 4 \sin (2 x) \cos (2 x) + 16 \sin^{2} (x) \cos^{2} (x)$

Suma $4 \sin (2 x) \cos (2 x)$ y $4 \sin (2 x) \cos (2 x)$ .

$16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 8 \sin (2 x) \cos (2 x) + 16 \sin^{2} (x) \cos^{2} (x)$

Step 2

Simplifica mediante la adición de términos.

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Combina los términos opuestos en $16 \cos^{2} (x) \sin^{2} (x) - 8 \sin (2 x) \cos (2 x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 8 \sin (2 x) \cos (2 x) + 16 \sin^{2} (x) \cos^{2} (x)$ .

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Suma $- 8 \sin (2 x) \cos (2 x)$ y $8 \sin (2 x) \cos (2 x)$ .

$16 \cos^{2} (x) \sin^{2} (x) + 0 + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 16 \sin^{2} (x) \cos^{2} (x)$

Suma $16 \cos^{2} (x) \sin^{2} (x)$ y $0$ .

$16 \cos^{2} (x) \sin^{2} (x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 16 \sin^{2} (x) \cos^{2} (x)$

Reordena los factores de $16 \sin^{2} (x) \cos^{2} (x)$ .

$16 \cos^{2} (x) \sin^{2} (x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x) + 16 \cos^{2} (x) \sin^{2} (x)$

Suma $16 \cos^{2} (x) \sin^{2} (x)$ y $16 \cos^{2} (x) \sin^{2} (x)$ .

$32 \cos^{2} (x) \sin^{2} (x) + 4 \cos^{2} (2 x) + 4 \cos^{2} (2 x)$

Suma $4 \cos^{2} (2 x)$ y $4 \cos^{2} (2 x)$ .

$32 \cos^{2} (x) \sin^{2} (x) + 8 \cos^{2} (2 x)$