^ -1 [ (2 ^ -1 (3) ) ]= - Vidyadip

MCQ

$\cos ^{-1}\left[\cos \left(2 \cot ^{-1}(\sqrt{3})\right)\right]=$

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

✓

Answer

Correct option: D.

$\frac{\pi}{3}$

(d): We have, $\cos ^{-1}\left[\cos \left(2 \cot ^{-1}(\sqrt{3})\right)\right]$
$
\begin{array}{l}
=\cos ^{-1}\left[\cos 2\left(\frac{\pi}{6}\right)\right] \\
=\cos ^{-1}\left(\cos \left(\frac{\pi}{3}\right)\right)=\cos ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{3}
\end{array}
$

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