Question

Solve for $x$ :
$2{\tan }^{-1}\left(\cos x\right)={\tan }^{-1}\left(2cosecx\right)$

Answer 1

$2{\tan }^{-1}\left(\cos x\right)={\tan }^{-1}\left(2cosecx\right)$

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

$\frac{\cos x}{{\sin }^{2}x}=cosecx$

$cosecx(\cot x-1)=0$

$\cot x=1(\because cosecx\ne 0)$

$x=n\pi +\frac{\pi }{4},n\in Z$