# Identity proof

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• May 18th 2010, 02:03 PM
Sedgewick19
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?
• May 18th 2010, 02:08 PM
Deadstar
Quote:

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...

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

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

Then you have $\displaystyle \cos(4x) = \cos(2y) = 2\cos^2(y)-1 = 2\cos^2(2x) - 1$
• May 19th 2010, 06:31 AM
Sedgewick19
Thanks, I thought that may have been the way the solve the problem, but I was afraid that it was too easy.