If \(\sin^{-1}x+\sin^{-1}y=\frac{\pi}{2}\), then value of \(\cos^{-1}x+\cos^{-1}y\) is
Answer & explanation
Correct answer: option 1
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]
$⇒\left(\frac{\pi}{2}-\cos^{-1}x\right)+\left(\frac{\pi}{2}-\cos^{-1}y\right)=\frac{\pi}{2}$
$⇒-\left(\cos^{-1}x+\cos^{-1}y\right)=\frac{\pi}{2}-\pi$
$⇒\cos^{-1}x+\cos^{-1}y=\frac{\pi}{2}$