Question

How do I solve cos(2arcsin 2x) with a triangle? (Or just in general how to solve it.

Answer 1

\[\cos (2\sin^{-1} 2x)\]
DO you know the range of \(\sin^{-1} x\)?

Answer 2

Here's how I would do it.
t= arcsin(2x) means
there is an angle t such that sin(t)= 2x


so your problem is cos(2t)= cos^2(t)- sin^2(t)
use the drawing to figure out cos(t)