Evaluate: cos(2cos⁻¹ x + sin⁻¹ x) at x = 1/5.

Using $\sin^{-1}x = \frac{\pi}{2} - \cos^{-1}x$: $2\cos^{-1}x + \sin^{-1}x = \cos^{-1}x + \frac{\pi}{2}$ $\cos\left(\cos^{-1}x + \frac{\pi}{2}\right) = -\sin(\cos^{-1}x) = -\sqrt{1 - x^2}$ At $x = \frac{1}{5}$: $-\sqrt{1 - \frac{1}{25}} = -\frac{\sqrt{24}}{5}$