JEE Advance - Mathematics (1981 - No. 24)
Find the value of : $$\cos \left( {2{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \right)$$ at $$x = {1 \over 5}$$, where
$$0 \le {\cos ^{ - 1}}x \le \pi $$ and $$ - \pi /2 \le {\sin ^{ - 1}}x \le \pi /2$$.
$$0 \le {\cos ^{ - 1}}x \le \pi $$ and $$ - \pi /2 \le {\sin ^{ - 1}}x \le \pi /2$$.
$$\frac{-2\sqrt{6}}{5}$$
$$\frac{2\sqrt{6}}{5}$$
$$\frac{-\sqrt{6}}{5}$$
$$\frac{\sqrt{6}}{5}$$
$$\frac{2}{5}$$