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Inverse Trigonometric Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSInverse Trigonometric Functions1 Mark
Question
$\sin \left[\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right]$ is equal to
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Answer

We have,
$\sin \left[\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)\right]$
$=\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]=\sin \left[\frac{\pi}{3}+\frac{\pi}{6}\right]=\sin \left(\frac{\pi}{2}\right)=1$

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