Trigonometry from integration (simplifying) How do I simplify $$\frac14\sin(2\arccos(x))$$
to $$\frac12x\sqrt{1-x^2}$$
Note, it used to more complex I simplified it to this level, I think you have to use a triangle but im not sure...
Thank you,
Good Luck

If you let $\theta = \cos^{-1}(x)$, you can use the fact that $\sin(2\theta) = 2 \sin \theta \cos \theta$. You then need to write $\sin \theta$ and $\cos \theta$ in terms of $x$ in order to get the result you are looking for (and you can certainly use a triangle to help with that part).
