If $\sin^{-1}\big(x-\large\frac{x^2}{2}+\frac{x^3}{4}-........)$$+\cos^{-1}(x^2-\large\frac{x^4}{2}+\frac{x^6}{4}.......)=\large\frac{\pi}{2}$.For $0<\mid x\mid<\sqrt 2$ then $x$ equals

Question

$\begin{array}{1 1}(a)\;\large\frac{1}{2}&(b)\;1\\(c)\;-\large\frac{1}{2}&(d)\;-1\end{array}$