# If $\sin^{-1}x+\sin^{-1}y=\large\frac{\pi}{2}$ then $\cos^{-1}x+\cos^{-1}y$ is equal to

$(a)\;\large\frac{\pi}{2}$$\qquad(b)\;\large\frac{\pi}{4}$$\qquad(c)\;\pi\qquad(d)\;\large\frac{3\pi}{4}$

Given :
$\sin^{-1}x+\sin^{-1}y=\large\frac{\pi}{2}$
$\large\frac{\pi}{2}-$$\cos^{-1}x+\large\frac{\pi}{2}$$-\sin^{-1}y=\large\frac{\pi}{2}$
$\cos^{-1}x+\cos^{-1}y=\large\frac{\pi}{2}$
Hence (a) is the correct answer.