I need to know how

$\displaystyle 1-\cos(2\arcsin\frac{s}{4}) = \frac{s^{2}}{8} $

and how

$\displaystyle \sin(2\arcsin\frac{s}{4}) = 2\frac{s}{4}\sqrt{1-\frac{s^{2}}{16}}$

I know the rule $\displaystyle \cos\arcsin(x)) = \sqrt{1-x^{2}} $ but don't know what to do with the 2 before the inverse trig functions eah time.

Thanks