# How do you get the exact value of cos[2 sin^-1(sqrt2 / 2)]?

$\sin x = \frac{\sqrt{2}}{2}$
$\arcsin x = \frac{\pi}{4}$
$\cos \left(\left(2\right) \left(\frac{\pi}{4}\right)\right) = \cos \left(\frac{\pi}{2}\right) = 0$