# Inverse Trig Functions with Double Angle Formulas

I am studying for a quiz tomorrow and one of the sections I am studying involves rewriting quantities as algebraic expressions of $x$. One of the problems I am having trouble with is:

$$\sin (2\arccos x))$$

I know I have to use the double angle formula, but my problem is that I do not know to use the double angle formula for cos or sin. I was also wondering when would be the appropriate time to use it. I would appreciate any help!

## 1 Answer

Let $t = \arccos x \implies x = \cos t$ and $0 < t < \pi$. So $\sin 2t = 2\sin t\cos t = 2x\sqrt{1 - x^2}$.