If $x=\frac{1}{5}$, the value of $\cos(\cos^{-1}x+2\sin^{-1}x)$ is:
Answer & explanation
Correct answer: option 3
$\cos(\cos^{-1}\frac{1}{5}+2\sin^{-1}\frac{1}{5})=\cos[\cos^{-1}\frac{1}{5}+\sin^{-1}\frac{1}{5}+\sin^{-1}\frac{1}{5}]$
$\cos[\frac{π}{2}+\sin^{-1}\frac{1}{5}]=-\sin[\sin^{-1}\frac{1}{5}]=-\frac{1}{5}$