A) 0
B) \[\frac{\pi }{2}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{10\pi }{3}\]
Correct Answer: A
Solution :
\[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \sin \frac{5\pi }{3} \right)\] \[={{\cos }^{-1}}\left[ \cos \left( 2\pi -\frac{\pi }{3} \right) \right]+{{\sin }^{-1}}\left[ \sin \left( 2\pi -\frac{\pi }{3} \right) \right]\] \[=\frac{\pi }{3}-\frac{\pi }{3}=0\].
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