If $4 sin^{-1} x + cos^{-1}x = \pi , $ then x equals

$\frac{1}{2}$

The correct answer is Option 1: $\frac{1}{2}$

Given:

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

Use identity:

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

Substitute:

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

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

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

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

Final value:

$x = \sin \left( \frac{\pi}{6} \right) = \frac{1}{2}$