If $\sqrt{\sin x} + \cos x = 0$, then $\sin x$ is equal to :

Question

( A ) $\frac{\sqrt{5} + 1}{2}$
( B ) $\frac{\sqrt{5} - 1}{2}$
( C ) $\frac{\sqrt{5} - 1}{8}$
( D ) $\frac{\sqrt{5} + 1}{8}$