Trigonometry Examples

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

Step 1

Apply the sine double-angle identity.

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

Step 2

Cancel the common factor of $\sin (x)$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $2 \cos (x)$ by $1$ .

$2 \cos (x) - \frac{\cos (2 x)}{\cos (x)}$

Step 3

Rewrite $\frac{\cos (2 x)}{\cos (x)}$ as a product.

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

Step 4

Write $\cos (2 x)$ as a fraction with denominator $1$ .

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

Step 5

Simplify.

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Step 5.1

Divide $\cos (2 x)$ by $1$ .

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

Step 5.2

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$2 \cos (x) - (\cos (2 x) \sec (x))$

$2 \cos (x) - \cos (2 x) \sec (x)$