For x∈[1,1], if 4 sin^-1x + cos^-1x = π then x is equal to

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

$4\sin^{-1}x+\cos^{-1}x=\pi$

Use the identity:

$\cos^{-1}x=\frac{\pi}{2}-\sin^{-1}x$

Substitute:

$4\sin^{-1}x+\left(\frac{\pi}{2}-\sin^{-1}x\right)=\pi$

Combine like terms:

$3\sin^{-1}x+\frac{\pi}{2}=\pi$

So:

$3\sin^{-1}x=\frac{\pi}{2}$

$\sin^{-1}x=\frac{\pi}{6}$

Therefore:

$x=\sin\left(\frac{\pi}{6}\right)$

$x=\frac{1}{2}$