Choose the correct answer from the given four options. The value … - Vidyadip

MCQ

Choose the correct answer from the given four options. The value of the expression $2\sec^{-1}2+\sin^{-1}\Big(\frac{1}{2}\Big)$ is:

A
$\frac{\pi}{6}$
✓
$\frac{5\pi}{6}$
C
$\frac{7\pi}{6}$
D
$1$

✓

Answer

Correct option: B.

$\frac{5\pi}{6}$

We have, $2\sec^{-1}2+\sin^{-1}\Big(\frac{1}{2}\Big)$
$=2\sec^{-1}\sec\frac{\pi}{3}+\sin^{-1}\sin\frac{\pi}{6}$
$=2\frac{\pi}{3}+\frac{\pi}{6}$
$[\because \sec^{-1}(\sec\text{x})=\text{x} $ and $ \sin^{-1}(\sin\text{x})=\text{x}]$
$=\frac{4\pi+\pi}{6}$
$=\frac{5\pi}{6}$

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