Question

Solve the following equation
$2tan^{-1}(cosx) = tan^{-1}(2cosecx)$

• A. $0$
• B. $\pi/3$
• C. $\pi/4$
• D. $\pi/2$

Answer 1

Answer: (C)

We have, $2\,tan^{-1}\left(cos\,x\right) = tan^{-1}\left(2cosec\,x\right)$
$\Rightarrow tan^{-1} \frac{2\,cos\,x}{1-cos^{2}\,x} = tan^{-1}\left(2cosec\,x\right)$
$\Rightarrow \frac{2\,cos\,x}{sin^{2}\,x} = 2cosec\,x$
$\Rightarrow tan\,x = 1$
$\Rightarrow x = \frac{\pi}{4}$