If 2 $ an^{- 1}{\left( \cos\ x ight) = an^{- 1}{(2\ cosec\ x),}}\$then the value of $x$ is

Question

If 2 $	an^{- 1}{\left( \cos\ x ight) = 	an^{- 1}{(2\ cosec\ x),}}\$then the value of $x$ is

Dr. Abubacker · Accepted Answer

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

Q. If 2 $\tan^{- 1}{\left( \cos\ x \right) = \tan^{- 1}{(2\ cosec\ x),}}\$then the value of $x$ is

Explanation

Reviewed by Dr. Abubacker

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