Trigonometría Ejemplos

$\cos (x + y) \cos (x - y)$

Step 1

Aplica la suma de la razón de los ángulos $\cos (x + y) = \cos (x) \cos (y) - \sin (x) \sin (y)$ .

$(\cos (x) \cos (y) - \sin (x) \sin (y)) \cos (x - y)$

Step 2

Aplica la diferencia de la razón de los ángulos $\cos (x - y) = \cos (x) \cos (y) + \sin (x) \sin (y)$ .

$(\cos (x) \cos (y) - \sin (x) \sin (y)) (\cos (x) \cos (y) + \sin (x) \sin (y))$

Step 3

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

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Aplica la propiedad distributiva.

$\cos (x) \cos (y) (\cos (x) \cos (y) + \sin (x) \sin (y)) - \sin (x) \sin (y) (\cos (x) \cos (y) + \sin (x) \sin (y))$

Aplica la propiedad distributiva.

$\cos (x) \cos (y) (\cos (x) \cos (y)) + \cos (x) \cos (y) (\sin (x) \sin (y)) - \sin (x) \sin (y) (\cos (x) \cos (y) + \sin (x) \sin (y))$

Aplica la propiedad distributiva.

$\cos (x) \cos (y) (\cos (x) \cos (y)) + \cos (x) \cos (y) (\sin (x) \sin (y)) - \sin (x) \sin (y) (\cos (x) \cos (y)) - \sin (x) \sin (y) (\sin (x) \sin (y))$

Step 4

Simplifica los términos.

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Combina los términos opuestos en $\cos (x) \cos (y) (\cos (x) \cos (y)) + \cos (x) \cos (y) (\sin (x) \sin (y)) - \sin (x) \sin (y) (\cos (x) \cos (y)) - \sin (x) \sin (y) (\sin (x) \sin (y))$ .

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Reordena los factores en los términos $\cos (x) \cos (y) (\sin (x) \sin (y))$ y $- \sin (x) \sin (y) (\cos (x) \cos (y))$ .

$\cos (x) \cos (y) (\cos (x) \cos (y)) + \cos (x) \cos (y) \sin (x) \sin (y) - \cos (x) \cos (y) \sin (x) \sin (y) - \sin (x) \sin (y) (\sin (x) \sin (y))$

Resta $\cos (x) \cos (y) \sin (x) \sin (y)$ de $\cos (x) \cos (y) \sin (x) \sin (y)$ .

$\cos (x) \cos (y) (\cos (x) \cos (y)) + 0 - \sin (x) \sin (y) (\sin (x) \sin (y))$

Suma $\cos (x) \cos (y) (\cos (x) \cos (y))$ y $0$ .

$\cos (x) \cos (y) (\cos (x) \cos (y)) - \sin (x) \sin (y) (\sin (x) \sin (y))$

Simplifica cada término.

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

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

$\cos^{1} (x) \cos (x) \cos (y) \cos (y) - \sin (x) \sin (y) (\sin (x) \sin (y))$

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

$\cos^{1} (x) \cos^{1} (x) \cos (y) \cos (y) - \sin (x) \sin (y) (\sin (x) \sin (y))$

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

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

Suma $1$ y $1$ .

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

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

$\cos^{2} (x) (\cos^{1} (y) \cos (y)) - \sin (x) \sin (y) (\sin (x) \sin (y))$

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

$\cos^{2} (x) (\cos^{1} (y) \cos^{1} (y)) - \sin (x) \sin (y) (\sin (x) \sin (y))$

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

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

Suma $1$ y $1$ .

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

Multiplica $- \sin (x) \sin (y) (\sin (x) \sin (y))$ .

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

$\cos^{2} (x) \cos^{2} (y) - (\sin^{1} (x) \sin (x)) \sin (y) \sin (y)$

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

$\cos^{2} (x) \cos^{2} (y) - (\sin^{1} (x) \sin^{1} (x)) \sin (y) \sin (y)$

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

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

Suma $1$ y $1$ .

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

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

$\cos^{2} (x) \cos^{2} (y) - \sin^{2} (x) (\sin^{1} (y) \sin (y))$

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

$\cos^{2} (x) \cos^{2} (y) - \sin^{2} (x) (\sin^{1} (y) \sin^{1} (y))$

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

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

Suma $1$ y $1$ .

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