question_answer

If \[{{\sin }^{-1}}\left( x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{4}-..... \right)+{{\cos }^{-1}}\left( {{x}^{2}}-\frac{{{x}^{4}}}{2}+\frac{{{x}^{6}}}{4}-..... \right)=\frac{\pi }{2},\] for \[0<|x|<\sqrt{2},\] then x equals:

A)  \[\frac{1}{2}\]                         

B)  1

C)  \[\frac{-1}{2}\]                        

D)  \[-1\]

E)  None of these