i know that cos(2x) = cos^2(x) - sin^2(x). But how does that then equal to 1-2sin^2(x)? and then = to 2cos^2(x) - 1. Can someone show me some sort of proof?
Well, sin^2(x) + cos^2(x) = 1 (i.e. the trig circle) and so cos^2(x) = 1 - sin^2(x).
Therefore, cos(2x) = 1 - sin^2(x) - sin^2(x)
= 1 - 2sin^2(x)
Then similarly with 2cos^2(x) - 1, except this time u make the sin^2(x) substitution.
