Mark the tick against the correct answer in the following:
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 $x=\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)$

$\Rightarrow x=\frac{\pi}{3}-\left(-\sin ^{-1}\left(\frac{1}{2}\right)\right)(\because \sin (-\theta)=-\sin (\theta)$

$\Rightarrow x=\frac{\pi}{3}-\left(-\frac{\pi}{6}\right)\left(\because \sin \frac{\pi}{6}=\frac{1}{2}\right)$

$\Rightarrow x=\frac{\pi}{3}+\frac{\pi}{6}$

$\Rightarrow x=\frac{3 \pi}{6}=\frac{\pi}{2}$

 

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