Question:
Mark the tick against the correct answer in the following:
$\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)=?$
A. 0
B. $\frac{2 \pi}{3}$
C. $\frac{\pi}{2}$
D. $\pi$
Solution:
To Find: The value of $\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)$
Now, let $x=\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)$
$\Rightarrow x=\frac{\pi}{3}-\left(-\sin ^{-1}\left(\frac{1}{2}\right)\right)(\because \sin (-\theta)=-\sin (\theta)$
$\Rightarrow x=\frac{\pi}{3}-\left(-\frac{\pi}{6}\right)\left(\because \sin \frac{\pi}{6}=\frac{1}{2}\right)$
$\Rightarrow x=\frac{\pi}{3}+\frac{\pi}{6}$
$\Rightarrow x=\frac{3 \pi}{6}=\frac{\pi}{2}$