A) \[\frac{1}{2}\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[\frac{\sqrt{3}}{2}\]
D) \[\frac{2}{\sqrt{3}}\]
E) \[\frac{3}{2}\]
Correct Answer: C
Solution :
\[4{{\cos }^{-1}}x+{{\sin }^{-1}}x=\pi \] \[\Rightarrow \] \[3{{\cos }^{-1}}x+{{\cos }^{-1}}x+{{\sin }^{-1}}x=\pi \] \[\Rightarrow \] \[3{{\cos }^{-1}}x=\frac{\pi }{2}\] \[\Rightarrow \] \[{{\cos }^{-1}}x=\frac{\pi }{6}\] \[\Rightarrow \] \[x=\cos \frac{\pi }{6}=\frac{\sqrt{3}}{2}\]
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