Mathematics - Inverse Trigonometric Function Question with Solution | TestHub

$\begin{array}{rl}& \cos \left[2{\cos }^{-1}x+{\sin }^{-1}x\right]\\ & =\cos \left[{\cos }^{-1}x+{\cos }^{-1}x+{\sin }^{-1}x\right]\\ & =\cos \left[{\cos }^{-1}x+\pi /2\right]=-\sin \left[{\cos }^{-1}x\right]\\ & =-\sin \left[{\sin }^{-1}\sqrt{1-x^2}\right]=-\sqrt{1-x^2}\\ & =-\sqrt{1-{\left(\frac{1}{5}\right)}^2}=-\sqrt{\frac{24}{25}}=-\frac{2\sqrt{6}}{5}\\ & \end{array}$