Question

Evaluate ${\tan }^{-1}\left(\frac{2\tan x}{1-\tan 2x}\right)$

Answer 1

Consider the following eq.

$ta{n}^{-1}\left(\frac{2tanx}{1-ta{n}^{2}x}\right)$

$ta{n}^{-1}\left(\frac{2tanx}{1-ta{n}^{2}x}\right)=ta{n}^{-1}\left(\tan 2x\right)$

$=2x$

Hence, this is the answer.