Question

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

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

Answer 1

Answer: (C)

We have, $2ta{n}^{-1}\left(cosx\right)=ta{n}^{-1}\left(2cosecx\right)$
$\Rightarrow ta{n}^{-1}\frac{2cosx}{1-co{s}^{2}x}=ta{n}^{-1}\left(2cosecx\right)$
$\Rightarrow \frac{2cosx}{si{n}^{2}x}=2cosecx$
$\Rightarrow tanx=1$
$\Rightarrow x=\frac{\pi }{4}$