If ^ -1 ( )=2 , then is equal to - Vidyadip

MCQ

If $\tan ^{-1}(\cot \theta)=2 \theta$, then $\theta$ is equal to

A
$\frac{\pi}{3}$
B
$\frac{\pi}{4}$
✓
$\frac{\pi}{6}$
D
None of these

✓

Answer

Correct option: C.

$\frac{\pi}{6}$

$\text { (c) }: \tan ^{-1}(\cot \theta)=2 \theta$
$\Rightarrow \cot \theta=\tan 2 \theta$
$\Rightarrow \cot \theta=\cot \left(\frac{\pi}{2}-2 \theta\right)$
$\Rightarrow \theta=\frac{\pi}{2}-2 \theta$
$\Rightarrow 3 \theta=\frac{\pi}{2}$
$\Rightarrow \theta=\frac{\pi}{6}$

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