Find the value of $\cos[2\cos^{-1}x+\sin^{-1}x]$ at $x=\large\frac{1}{5}$ where $0\leq \cos^{-1} x\leq \pi$ and $\large\frac{-\pi}{2}$$\leq \sin^{-1}x\leq \large\frac{\pi}{2}$

Question

$(a)\;\large\frac{2\sqrt 6}{5}$$\qquad(b)\;\large\frac{2}{5}$$\qquad(c)\;-\large\frac{2\sqrt 6}{5}$$\qquad(d)\;0$