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

MCQ

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

✓
$2 \pi / 3$
B
$\pi / 4$
C
$\pi / 6$
D
$\pi / 3$

✓

Answer

Correct option: A.

$2 \pi / 3$

$2 \sin ^{-1}\left(\frac{1}{2}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\frac{2 \pi}{6}+\frac{\pi}{3}$
$=\frac{\pi}{3}+\frac{\pi}{3}=\frac{2 \pi}{3} \quad [\because \sin \frac{\pi}{6}=\frac{1}{2}$ and $ \cot \frac{\pi}{3}=\frac{1}{\sqrt{3}}]$

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