If \(\sin^{-1}x+\sin^{-1}y=\frac{\pi}{2}\), then value of \(\cos^{-1}x+\cos^{-1}y\) is

\(\frac{\pi}{2}\)

The correct answer is Option (1) → \(\frac{\pi}{2}\)

\(\sin^{-1}x+\sin^{-1}y=\frac{\pi}{2}\)

$\cos^{-1}=\frac{\pi}{2}-\sin^{-1}a$  [Identity]

$⇒\left(\frac{\pi}{2}-\cos^{-1}x\right)+\left(\frac{\pi}{2}-\cos^{-1}y\right)=\frac{\pi}{2}$

$⇒-\left(\cos^{-1}x+\cos^{-1}y\right)=\frac{\pi}{2}-\pi$

$⇒\cos^{-1}x+\cos^{-1}y=\frac{\pi}{2}$