Mark the tick against the correct answer in the following:
Question:

Mark the tick against the correct answer in the following:

$\sin \left\{\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)\right\}=?$

A. 1

B. 0

C. $\frac{-1}{2}$

D. none of these

 

Solution:

To Find: The value of of $\sin \left\{\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)\right\}$

Let, $x=\sin \left\{\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)\right\}$

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

$\Rightarrow x=\sin \left(\frac{\pi}{3}+\frac{\pi}{6}\right)$

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

 

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