question_answer

lf \[f(x)=\int\limits_{0}^{\sin x}{{{\cos }^{-1}}}t\,dt\,+\int\limits_{0}^{\cos x}{{{\sin }^{-1}}t}\,dt,0<x<\frac{\pi }{2},\] than \[f\left( \frac{\pi }{4} \right)\]is

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

B)  \[1+\frac{\pi }{2\sqrt{2}}\]

C)  \[1\]                

D)  \[1-\frac{\pi }{\sqrt{2}}\]