A) \[\frac{1}{2}\]
B) \[-1\]
C) \[1\]
D) \[-\frac{1}{2}\]
Correct Answer: A
Solution :
[a] Given that \[{{\cos }^{-1}}x=2{{\sin }^{-1}}x\] \[\Rightarrow \frac{\pi }{2}-{{\sin }^{-1}}x=2{{\sin }^{-1}}x\] \[\Rightarrow \frac{\pi }{2}=3{{\sin }^{-1}}x\Rightarrow {{\sin }^{-1}}x=\frac{\pi }{6}\] So, \[x=\sin \frac{\pi }{6}=\frac{1}{2}\]
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