Question

Solve $2{\cos }^{-1}x+{\sin }^{-1}x=\frac{11\pi }{6}$

Answer 1

Given, $2{\cos }^{-1}x+{\sin }^{-1}x=\frac{11\pi }{6}$
$\Rightarrow {\cos }^{-1}x+\frac{\pi }{2}=\frac{11\pi }{6}$
$\Rightarrow {\cos }^{-1}x=\frac{8\pi }{6}=\pi +\frac{\pi }{3}$
This is not possible since $0\le {\cos }^{-1}x\le \pi$