What is the value of $\cos\left(2\sin^{-1} \frac{1}{2}\right)$?

Explanation

1. 01

   $\sin^{-1} \frac{1}{2} = \frac{\pi}{6}$, so the angle is $\frac{\pi}{3}$.

2. 02

   $\cos \frac{\pi}{3} = \frac{1}{2}$.