Question

If $2ta{n}^{-1}\left(cosx\right)=ta{n}^{-1}\left(2cosecx\right)$ then the value of x is

• A. 3π/4
• B. π/4
• C. π/3
• D. π/8

Answer 1

The correct option is B

π/4

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