A) \[\frac{\pi }{6}\]
B) \[\frac{5\pi }{6}\]
C) \[\frac{7\pi }{6}\]
D) None of these
Correct Answer: A
Solution :
\[{{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}\] \[={{\sin }^{-1}}\left\{ \sin \left( \pi -\frac{\pi }{6} \right) \right\}\] \[[\because \,sin\,(\pi -\theta )=sin\theta ]\] \[={{\sin }^{-1}}\left\{ \sin \frac{\pi }{6} \right\}\] \[\because \,[Principal\,value]\in [0,\,\pi \text{/}2]\] \[=\frac{\pi }{6}\] which is the required principal value.
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