Question

Solve for $x$:

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

Answer 1

Given,

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

$\Rightarrow 3{\sin }^{-1}x+({\sin }^{-1}x+{\cos }^{-1}x)=\pi$

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

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

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

$\Rightarrow x=\sin \frac{\pi }{6}$

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