$\lim\limits_{x\to {-1}}\large\frac{\sqrt{\pi}-\sqrt{\cos^{-1}x}}{\sqrt{x+1}}$ is given by

Question

$(a)\;\large\frac{1}{\sqrt{\pi}}$$\qquad(b)\;\large\frac{1}{\sqrt{2\pi}}$$\qquad(c)\;1\qquad(d)\;0$