Trigonometria Exemplos

\frac{sin (8 x)}{8 sin (x)} - cos (x) cos (2 x) cos (4 x)

$\frac{\sin (8 x)}{8 \sin (x)} - \cos (x) \cos (2 x) \cos (4 x)$

Etapa 1

Separe as frações.

\frac{1}{8} \cdot \frac{sin (8 x)}{sin (x)} - cos (x) cos (2 x) cos (4 x)

$\frac{1}{8} \cdot \frac{\sin (8 x)}{\sin (x)} - \cos (x) \cos (2 x) \cos (4 x)$

Etapa 2

Reescreva

\frac{sin (8 x)}{sin (x)}

$\frac{\sin (8 x)}{\sin (x)}$ como um produto.

\frac{1}{8} (sin (8 x) \frac{1}{sin (x)}) - cos (x) cos (2 x) cos (4 x)

$\frac{1}{8} (\sin (8 x) \frac{1}{\sin (x)}) - \cos (x) \cos (2 x) \cos (4 x)$

Etapa 3

Escreva

sin (8 x)

$\sin (8 x)$ como uma fração com denominador

1

$1$ .

\frac{1}{8} (\frac{sin (8 x)}{1} \cdot \frac{1}{sin (x)}) - cos (x) cos (2 x) cos (4 x)

$\frac{1}{8} (\frac{\sin (8 x)}{1} \cdot \frac{1}{\sin (x)}) - \cos (x) \cos (2 x) \cos (4 x)$

Etapa 4

Simplifique.

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Etapa 4.1

Divida

sin (8 x)

$\sin (8 x)$ por

1

$1$ .

\frac{1}{8} (sin (8 x) \frac{1}{sin (x)}) - cos (x) cos (2 x) cos (4 x)

$\frac{1}{8} (\sin (8 x) \frac{1}{\sin (x)}) - \cos (x) \cos (2 x) \cos (4 x)$

Etapa 4.2

Converta de

\frac{1}{sin (x)}

$\frac{1}{\sin (x)}$ em

csc (x)

$\csc (x)$ .

\frac{1}{8} (sin (8 x) csc (x)) - cos (x) cos (2 x) cos (4 x)

$\frac{1}{8} (\sin (8 x) \csc (x)) - \cos (x) \cos (2 x) \cos (4 x)$

\frac{1}{8} (sin (8 x) csc (x)) - cos (x) cos (2 x) cos (4 x)

$\frac{1}{8} (\sin (8 x) \csc (x)) - \cos (x) \cos (2 x) \cos (4 x)$

Etapa 5

Multiplique

\frac{1}{8} (sin (8 x) csc (x))

$\frac{1}{8} (\sin (8 x) \csc (x))$ .

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Etapa 5.1

Combine

sin (8 x)

$\sin (8 x)$ e

\frac{1}{8}

$\frac{1}{8}$ .

\frac{sin (8 x)}{8} csc (x) - cos (x) cos (2 x) cos (4 x)

$\frac{\sin (8 x)}{8} \csc (x) - \cos (x) \cos (2 x) \cos (4 x)$

Etapa 5.2

Combine

\frac{sin (8 x)}{8}

$\frac{\sin (8 x)}{8}$ e

csc (x)

$\csc (x)$ .

\frac{sin (8 x) csc (x)}{8} - cos (x) cos (2 x) cos (4 x)

$\frac{\sin (8 x) \csc (x)}{8} - \cos (x) \cos (2 x) \cos (4 x)$

\frac{sin (8 x) csc (x)}{8} - cos (x) cos (2 x) cos (4 x)

$\frac{\sin (8 x) \csc (x)}{8} - \cos (x) \cos (2 x) \cos (4 x)$