1. Identity proof

Hello,

I am having trouble simplifying this identity [cos4x= 2cos^2 2x-1]. I thought I could solve it with the double angle identity, but the 2x seems to be getting in the way. Can I remove the 2x and multiply it by the identity cos2x?

2. Originally Posted by Sedgewick19

Hello,

I am having trouble proving this identity [cos4x= 2cos^2 2x-1]. I thought I could solve it with the double angle identity, but the 2x seems to be getting in the way. Can I remove the 2x and multiply it by the identity cos2x?
It's just a simple substitution really...

$\cos(2x)= 2\cos^2(x)-1$ you know.

Well in the $4x$ case, just set $y = 2x$.

Then you have $\cos(4x) = \cos(2y) = 2\cos^2(y)-1 = 2\cos^2(2x) - 1$

3. Thanks, I thought that may have been the way the solve the problem, but I was afraid that it was too easy.