If 2tan^ -1 (cosx) = tan^ -1 (cosec^2x) then x = - Vidyadip

MCQ

If $2tan^{-1}(cosx) = tan^{-1}(cosec^2x)$ then $x =$

A
$\frac{\pi}{2}$
B
$\pi$
C
$\frac{\pi}{6}$
✓
$\frac{\pi}{3}$

✓

Answer

Correct option: D.

$\frac{\pi}{3}$

d
$\tan ^{-1} \frac{2 \cos x}{1-\cos ^{2} x}=\tan ^{-1}\left(\frac{1}{\sin ^{2} x}\right)$

$\Rightarrow \frac{2 \cos x}{\sin ^{2} x}=\frac{1}{\sin ^{2} x} \Rightarrow 2 \cos x=1 \Rightarrow x=\frac{\pi}{3}$

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