Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

Rewrite $\frac{\sin (8 x)}{\sin (x)}$ as a product.

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

Step 3

Write $\sin (8 x)$ as a fraction with denominator $1$ .

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

Step 4

Simplify.

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Step 4.1

Divide $\sin (8 x)$ by $1$ .

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

Step 4.2

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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