Inverse circular functions,Principal values of ${\sin }^{-1}x,{cos}^{-1}x,{\tan }^{-1}x$.
${\tan }^{-1}x+{\tan }^{-1}y={\tan }^{-1}\frac{x+y}{1-xy}$,      $xy<1$
       $\pi +{\tan }^{-1}\frac{x+y}{1-xy}$,         $xy>1$.
Evaluate the following :
(a) $\sin \left[\frac{\pi }{3}-{\sin }^{-1}\left(-\frac{1}{2}\right)\right]$
(b) $\sin \left[\frac{\pi }{2}-{\sin }^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]$

The value of ${\cot }^{-1}\left[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{(1-\sin x)}-\sqrt{(1+\sin x)}}\right]$ is