A) \[\frac{\pi }{6}\]
B) \[\frac{2\pi }{3}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{5\pi }{6}\]
Correct Answer: C
Solution :
\[{{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}+{{\tan }^{-1}}\left\{ \tan \frac{\pi }{6} \right\}\] \[={{\sin }^{-1}}\left\{ \sin \left( \pi -\frac{\pi }{6} \right) \right\}+\frac{\pi }{6}\] \[={{\sin }^{-1}}\,\left\{ \sin \frac{\pi }{6} \right\}+\frac{\pi }{6}\] \[=\frac{\pi }{6}+\frac{\pi }{6}=\frac{2\pi }{6}=\frac{\pi }{3}\]
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