Algebra Examples

$\frac{\tan (2 x)}{\tan (x)}$

Step 1

Rewrite $\tan (x)$ in terms of sines and cosines.

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

Step 2

Rewrite $\tan (2 x)$ in terms of sines and cosines.

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

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (x)}{\cos (x)}$ .

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

Step 4

Simplify.

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Step 4.1

Convert from $\frac{\sin (2 x)}{\cos (2 x)}$ to $\tan (2 x)$ .

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

Step 4.2

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$\tan (2 x) \cot (x)$