Write the value of

Question:

Write the value of $\sin \left\{\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right\}$.

Solution:

We have

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

$=\sin \left\{\frac{\pi}{3}+\frac{\pi}{6}\right\}$

$=\sin \frac{\pi}{2}$

$=1$

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

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