A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{2\pi }{3}\]
Correct Answer: D
Solution :
[d] \[\because {{\cos }^{-1}}\left( \frac{1}{2} \right)+2{{\sin }^{-1}}\left( \frac{1}{2} \right)\] \[={{\cos }^{-1}}\left( \cos \frac{\pi }{3} \right)+2{{\sin }^{-1}}\left( \sin \frac{\pi }{6} \right)=\frac{\pi }{3}+2.\frac{\pi }{6}=\frac{2\pi }{3}\]Hence, option [d] is correct.
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