Question

Solve $\tan 2x=-\cot (x+\frac{\pi }{2})$

Answer 1

$\tan 2x=-\cot (x+\frac{\pi }{2})$

$\tan 2x=\tan x$

$\frac{2\tan x}{1-{\tan }^{2}x}=\tan x$

$\left(\tan x\right)(\frac{2}{1-{\tan }^{2}x}-1)=0$

$\left(\tan x\right)\left(\frac{1+{\tan }^{2}x}{1-{\tan }^{2}x}\right)=0$

$\Rightarrow \tan x=0$

$x=n\pi$