question_answer

The value of \[{{\sin }^{-1}}\left[ \cos \left( {{\sin }^{-1}}\sqrt{\,\,\left( \frac{2-\sqrt{3}}{4} \right)}+{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} \right) \right]\]is ___________.

A)  \[\frac{\pi }{2}\]                                   

B)  \[\frac{\pi }{4}\]

C)  \[\frac{\pi }{6}\]                                   

D)  \[\frac{\pi }{8}\]

E)  None of these