A) 0
B) \[\frac{1}{2}\]
C) \[-\frac{\sqrt{3}}{2}\]
D) \[\frac{1}{\sqrt{2}}\]
Correct Answer: B
Solution :
We know that \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi \] Þ \[3{{\sin }^{-1}}x+{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi \] Þ \[3{{\sin }^{-1}}x=\pi -\frac{\pi }{2}=\frac{\pi }{2}\] Þ \[{{\sin }^{-1}}x=\pi /6\]Þ \[x=\sin \frac{\pi }{6}=\frac{1}{2}\].
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