Trigonometría Ejemplos

{cos}^{2} (3 x) - {sin}^{2} (3 x)

$\cos^{2} (3 x) - \sin^{2} (3 x)$

Step 1

Dado que ambos términos son cuadrados perfectos, factoriza con la fórmula de la diferencia de cuadrados,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ , donde

a = cos (3 x)

$a = \cos (3 x)$ y

b = sin (3 x)

$b = \sin (3 x)$ .

(cos (3 x) + sin (3 x)) (cos (3 x) - sin (3 x))

$(\cos (3 x) + \sin (3 x)) (\cos (3 x) - \sin (3 x))$

Step 2

Simplifica los términos.

Toca para ver más pasos...

Simplifica cada término.

Toca para ver más pasos...

Usa la razón del ángulo triple para transformar

cos (3 x)

$\cos (3 x)$ a

4 {cos}^{3} (x) - 3 cos (x)

$4 \cos^{3} (x) - 3 \cos (x)$ .

(4 {cos}^{3} (x) - 3 cos (x) + sin (3 x)) (cos (3 x) - sin (3 x))

$(4 \cos^{3} (x) - 3 \cos (x) + \sin (3 x)) (\cos (3 x) - \sin (3 x))$

Aplica la razón del ángulo triple sinusoidal.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (cos (3 x) - sin (3 x))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (\cos (3 x) - \sin (3 x))$

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (cos (3 x) - sin (3 x))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (\cos (3 x) - \sin (3 x))$

Simplifica cada término.

Toca para ver más pasos...

Usa la razón del ángulo triple para transformar

cos (3 x)

$\cos (3 x)$ a

4 {cos}^{3} (x) - 3 cos (x)

$4 \cos^{3} (x) - 3 \cos (x)$ .

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) - sin (3 x))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) - \sin (3 x))$

Aplica la razón del ángulo triple sinusoidal.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) - (- 4 {sin}^{3} (x) + 3 sin (x)))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) - (- 4 \sin^{3} (x) + 3 \sin (x)))$

Aplica la propiedad distributiva.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) - (- 4 {sin}^{3} (x)) - (3 sin (x)))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) - (- 4 \sin^{3} (x)) - (3 \sin (x)))$

Multiplica

- 4

$- 4$ por

- 1

$- 1$ .

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - (3 sin (x)))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) + 4 \sin^{3} (x) - (3 \sin (x)))$

Multiplica

3

$3$ por

- 1

$- 1$ .

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - 3 sin (x))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) + 4 \sin^{3} (x) - 3 \sin (x))$

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - 3 sin (x))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) + 4 \sin^{3} (x) - 3 \sin (x))$

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - 3 sin (x))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) + 4 \sin^{3} (x) - 3 \sin (x))$

Step 3

Expande

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - 3 sin (x))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) + 4 \sin^{3} (x) - 3 \sin (x))$ mediante la multiplicación de cada término de la primera expresión por cada término de la segunda expresión.

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) + 4 {cos}^{3} (x) (4 {sin}^{3} (x)) + 4 {cos}^{3} (x) (- 3 sin (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (4 {cos}^{3} (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 sin (x) (4 {cos}^{3} (x)) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) + 4 \cos^{3} (x) (4 \sin^{3} (x)) + 4 \cos^{3} (x) (- 3 \sin (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (4 \cos^{3} (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (4 \cos^{3} (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Step 4

Simplifica los términos.

Toca para ver más pasos...

Combina los términos opuestos en

Toca para ver más pasos...

Reordena los factores en los términos

$4 \cos^{3} (x) (4 \sin^{3} (x))$ y

$- 4 \sin^{3} (x) (4 \cos^{3} (x))$ .

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) + 4 \cdot 4 \cos^{3} (x) \sin^{3} (x) + 4 \cos^{3} (x) (- 3 \sin (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \cdot 4 \cos^{3} (x) \sin^{3} (x) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (4 \cos^{3} (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Resta

$4 \cdot 4 \cos^{3} (x) \sin^{3} (x)$ de

$4 \cdot 4 \cos^{3} (x) \sin^{3} (x)$ .

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) + 4 \cos^{3} (x) (- 3 \sin (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) + 0 - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (4 \cos^{3} (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$0$ .

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) + 4 \cos^{3} (x) (- 3 \sin (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (4 \cos^{3} (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Reordena los factores en los términos

$4 \cos^{3} (x) (- 3 \sin (x))$ y

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

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cdot 4 \cos^{3} (x) \sin (x) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \cdot 4 \cos^{3} (x) \sin (x) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$- 3 \cdot 4 \cos^{3} (x) \sin (x)$ y

$3 \cdot 4 \cos^{3} (x) \sin (x)$ .

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 0 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$0$ .

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Simplifica cada término.

Toca para ver más pasos...

Reescribe con la propiedad conmutativa de la multiplicación.

$4 \cdot 4 \cos^{3} (x) \cos^{3} (x) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

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

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

Toca para ver más pasos...

Mueve

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

$4 \cdot 4 (\cos^{3} (x) \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Usa la regla de la potencia

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$4 \cdot 4 {\cos (x)}^{3 + 3} + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$3$ y

$3$ .

$4 \cdot 4 \cos^{6} (x) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$4$ por

$4$ .

$16 \cos^{6} (x) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

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

$\cos (x)$ sumando los exponentes.

Toca para ver más pasos...

Mueve

$\cos (x)$ .

$16 \cos^{6} (x) + 4 (\cos (x) \cos^{3} (x)) \cdot - 3 - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$\cos (x)$ por

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

Toca para ver más pasos...

Eleva

$\cos (x)$ a la potencia de

$1$ .

$16 \cos^{6} (x) + 4 (\cos^{1} (x) \cos^{3} (x)) \cdot - 3 - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Usa la regla de la potencia

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$16 \cos^{6} (x) + 4 {\cos (x)}^{1 + 3} \cdot - 3 - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$1$ y

$3$ .

$16 \cos^{6} (x) + 4 \cos^{4} (x) \cdot - 3 - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$- 3$ por

$4$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$\cos (x)$ por

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

Toca para ver más pasos...

Mueve

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

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 (\cos^{3} (x) \cos (x)) \cdot 4 - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

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

$\cos (x)$ .

Toca para ver más pasos...

Eleva

$\cos (x)$ a la potencia de

$1$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 (\cos^{3} (x) \cos^{1} (x)) \cdot 4 - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Usa la regla de la potencia

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 {\cos (x)}^{3 + 1} \cdot 4 - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$3$ y

$1$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 \cos^{4} (x) \cdot 4 - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$4$ por

$- 3$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$- 3 \cos (x) (- 3 \cos (x))$ .

Toca para ver más pasos...

Multiplica

$- 3$ por

$- 3$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos (x) \cos (x) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Eleva

$\cos (x)$ a la potencia de

$1$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 (\cos^{1} (x) \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Eleva

$\cos (x)$ a la potencia de

$1$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 (\cos^{1} (x) \cos^{1} (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Usa la regla de la potencia

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 {\cos (x)}^{1 + 1} - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$1$ y

$1$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$4$ por

$- 3$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$- 3$ por

$- 3$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$- 3$ por

$- 4$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Reescribe con la propiedad conmutativa de la multiplicación.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \cdot 4 \sin^{3} (x) \sin^{3} (x) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

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

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

Toca para ver más pasos...

Mueve

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

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \cdot 4 (\sin^{3} (x) \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Usa la regla de la potencia

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \cdot 4 {\sin (x)}^{3 + 3} - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$3$ y

$3$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \cdot 4 \sin^{6} (x) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$- 4$ por

$4$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

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

$\sin (x)$ sumando los exponentes.

Toca para ver más pasos...

Mueve

$\sin (x)$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 (\sin (x) \sin^{3} (x)) \cdot - 3 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$\sin (x)$ por

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

Toca para ver más pasos...

Eleva

$\sin (x)$ a la potencia de

$1$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 (\sin^{1} (x) \sin^{3} (x)) \cdot - 3 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Usa la regla de la potencia

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 {\sin (x)}^{1 + 3} \cdot - 3 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Suma

$1$ y

$3$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 \sin^{4} (x) \cdot - 3 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$- 3$ por

$- 4$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$- 3$ por

$3$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

Multiplica

$\sin (x)$ por

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

Toca para ver más pasos...

Mueve

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

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 3 (\sin^{3} (x) \sin (x)) \cdot 4 + 3 \sin (x) (- 3 \sin (x))$

Multiplica

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

$\sin (x)$ .

Toca para ver más pasos...

Eleva

$\sin (x)$ a la potencia de

$1$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 3 (\sin^{3} (x) \sin^{1} (x)) \cdot 4 + 3 \sin (x) (- 3 \sin (x))$

Usa la regla de la potencia

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 3 {\sin (x)}^{3 + 1} \cdot 4 + 3 \sin (x) (- 3 \sin (x))$

Suma

$3$ y

$1$ .

Multiplica

$4$ por

$3$ .

Multiplica

$3 \sin (x) (- 3 \sin (x))$ .

Toca para ver más pasos...

Multiplica

$- 3$ por

$3$ .

Eleva

$\sin (x)$ a la potencia de

$1$ .

Eleva

$\sin (x)$ a la potencia de

$1$ .

Usa la regla de la potencia

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

Suma

$1$ y

$1$ .

Simplifica mediante la adición de términos.

Toca para ver más pasos...

Combina los términos opuestos en

Toca para ver más pasos...

Reordena los factores en los términos

$- 12 \cos (x) \sin^{3} (x)$ y

$12 \sin^{3} (x) \cos (x)$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \sin^{3} (x) \cos (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

Suma

$- 12 \sin^{3} (x) \cos (x)$ y

$12 \sin^{3} (x) \cos (x)$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 9 \cos (x) \sin (x) + 0 - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

Suma

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 9 \cos (x) \sin (x)$ y

$0$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 9 \cos (x) \sin (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

Reordena los factores en los términos

$9 \cos (x) \sin (x)$ y

$- 9 \sin (x) \cos (x)$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 9 \cos (x) \sin (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \cos (x) \sin (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

Resta

$9 \cos (x) \sin (x)$ de

$9 \cos (x) \sin (x)$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 0 - 16 \sin^{6} (x) + 12 \sin^{4} (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

Suma

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x)$ y

$0$ .

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

Resta

$12 \cos^{4} (x)$ de

$- 12 \cos^{4} (x)$ .

$16 \cos^{6} (x) - 24 \cos^{4} (x) + 9 \cos^{2} (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

Suma

$12 \sin^{4} (x)$ y

$12 \sin^{4} (x)$ .

$16 \cos^{6} (x) - 24 \cos^{4} (x) + 9 \cos^{2} (x) - 16 \sin^{6} (x) + 24 \sin^{4} (x) - 9 \sin^{2} (x)$