# How do you simplify  cos(sin^-1(2/x))?

$| x | \ge 2 \mathmr{and} \cos \left({\sin}^{- 1} \left(\frac{2}{x}\right)\right) = \pm \frac{\sqrt{{x}^{2} - 4}}{x}$
Let $a = {\sin}^{- 1} \left(\frac{2}{x}\right)$. Then $\sin a = \left(\frac{2}{x}\right) \mathmr{and} \cos a = \pm \frac{\sqrt{{x}^{2} - 4}}{x}$.
So, $\cos \left({\sin}^{- 1} \left(\frac{2}{x}\right)\right) = \cos a = \pm \frac{\sqrt{{x}^{2} - 4}}{x}$.