Find the value of ^ -1 (2 (2 ^ -1 1 2 ) ). - Vidyadip

MCQ

Find the value of $\tan ^{-1}\left(2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right)$.

A
$\frac{\pi}{3}$
✓
$\frac{\pi}{4}$
C
$\frac{\pi}{2}$
D
$\frac{\pi}{6}$

✓

Answer

Correct option: B.

$\frac{\pi}{4}$

We have,
$\tan ^{-1}\left\{2 \cos \left(2 \sin ^{-1}\left(\frac{1}{2}\right)\right)\right\}=\tan ^{-1}\left\{2 \cos \left(2 \times \frac{\pi}{6}\right)\right\}$
$=\tan ^{-1}\left\{2 \cos \frac{\pi}{3}\right\}=\tan ^{-1}\left[2 \times \frac{1}{2}\right]=\tan ^{-1} 1=\frac{\pi}{4}$

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