The value of ^ -1 ( ^ -1 2 3 ) is - Vidyadip

MCQ

The value of $\tan ^{-1}\left\{\sin \left(\cos ^{-1} \sqrt{\frac{2}{3}}\right)\right\}$ is

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

✓

Answer

Correct option: D.

$\frac{\pi}{6}$

(D) $\tan ^{-1}\left\{\sin \left(\cos ^{-1} \sqrt{\frac{2}{3}}\right)\right\}$
$=\tan ^{-1}\left\{\sin \left(\sin ^{-1} \sqrt{\frac{1}{3}}\right)\right\}$ $\ldots\left[\because \cos ^{-1} x=\sin ^{-1} \sqrt{1-x^2}\right]$
$=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\frac{\pi}{6}$

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