Q. If $2\tan^{- 1}{\left( \cos x \right) = \tan^{- 1}{(2\ cosec\ x)}}$, then the value of $x$ is
A) $\frac{3\pi}{4}$
B) $\frac{\pi}{4}$
C) $\frac{\pi}{3}$
D) None of these
Explanation
(b)
Given, $2\tan^{- 1}{\left( \cos x \right) = \tan^{- 1}{(2\ cosec\ x)}}$
$\therefore\ \tan^{- 1}{\left( \frac{2\cos x}{1 - \cos^{2}x} \right) = \tan^{- 1}{(2\ cosec\ x)}}$
$\Rightarrow \ \ \frac{2\cos x}{1 - \cos^{2}x} = 2cosec\ x$
$\Rightarrow \ \ \frac{2\cos x}{\sin^{2}x} = 2cosec\ x$
$\Rightarrow \ \sin{x = \cos{x\ \ \Rightarrow \ \ \ x = \frac{\pi}{4}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.