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

✓

Answer

Correct option: B.

$\frac{\pi}{4}$

b
Let $\sin ^{-1} \frac{1}{2}=x$

Then, $\sin x=\frac{1}{2}=\sin \left(\frac{\pi}{6}\right)$

$\therefore \sin ^{-1} \frac{1}{2}=\frac{\pi}{6}$

$\therefore \tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]$

$=\tan ^{-1}\left[2 \cos \left(2 \times \frac{\pi}{6}\right)\right]$

$=\tan ^{-1}\left[2 \cos \frac{\pi}{3}\right]$

$=\tan ^{-1}\left[2 \times \frac{1}{2}\right]$

$=\tan ^{-1} 1=\frac{\pi}{4}$

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