If $4 sin^{-1} x + cos^{-1}x = \pi , $ then x equals
Answer & explanation
Correct answer: option 1
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:
$x = \sin \left( \frac{\pi}{6} \right) = \frac{1}{2}$