^ -1 (-1 2 )+2 ^ -1 (-1 2 ) is equal to - Vidyadip

MCQ

$\cos ^{-1}\left(\frac{-1}{2}\right)+2 \sin ^{-1}\left(\frac{-1}{2}\right)$ is equal to

✓
$\frac{\pi}{3}$
B
$\frac{2 \pi}{3}$
C
$\frac{3 \pi}{4}$
D
$\frac{5 \pi}{8}$

✓

Answer

Correct option: A.

$\frac{\pi}{3}$

(a) : Principal value of $\cos ^{-1}\left(\frac{-1}{2}\right)$ is $\frac{2 \pi}{3}$
and principal value of $\sin ^{-1}\left(\frac{-1}{2}\right)$ is $\left(\frac{-\pi}{6}\right)$.
$\therefore \quad \cos ^{-1}\left(\frac{-1}{2}\right)+2 \sin ^{-1}\left(\frac{-1}{2}\right)$
$=\frac{2 \pi}{3}+\left(2 \times \frac{-\pi}{6}\right)=\frac{2 \pi}{3}-\frac{\pi}{3}=\frac{\pi}{3}$

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