• # question_answer If$x=1/5$¸the value of$\cos ({{\cos }^{-1}}x+2{{\sin }^{-1}}x)$is A) $-\sqrt{\frac{24}{25}}$                    B) $\sqrt{\frac{24}{25}}$C) $-\frac{1}{5}$                                  D) $\frac{1}{5}$

The given expression is equal to             $\cos ({{\cos }^{-1}}x+{{\sin }^{-1}}x+{{\sin }^{-1}}x)$ $=\cos \left( \frac{\pi }{2}+{{\sin }^{-1}}x \right)=-\sin ({{\sin }^{-1}}x)=-x=-\frac{1}{5}$ $[\text{Using}{{\cos }^{-1}}x+{{\sin }^{-1}}x=\frac{\pi }{2}]$