The trigonometric equation $\sin^{-1}x = 2 \sin^{-1} a$, has a solution for :

Question

( A ) all real values of $a$
( B ) $|a| \geq \frac{1}{\sqrt{2}}$
( C ) $|a| < \frac{1}{2}$
( D ) $\frac{1}{2} < |a|<\frac{1}{\sqrt{2}}$</span>