A) \[\frac{2\pi }{3}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{6}\]
D) \[\pi \]
Correct Answer: B
Solution :
\[{{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{2\pi }{3}\]\[\Rightarrow \frac{\pi }{2}-{{\cos }^{-1}}x+\frac{\pi }{2}-{{\cos }^{-1}}y=\frac{2\pi }{3}\] Þ \[{{\cos }^{-1}}x+{{\cos }^{-1}}y=\pi -\frac{2\pi }{3}=\frac{\pi }{3}\].
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