Simplify (tan(2x))/(tan(x))

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

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

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

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

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

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

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

Simplify.

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

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

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

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