Question

Prove that
cos4x=8cos^4x-8cos^2x+1

so I'm guessing you begin with the left side cos4x=cos2(2x) then im kinda lost

Answer 1

You began the problem correctly. Continue to use the cos "double angle" formula, applying it twice.
cos4x = cos[2(2x)] = 2 cos^2(2x) - 1
= 2(2cos^2 x - 1)^2 -1
= 2*[4 cos^4 x -4cos^2 x +1) -1
= 8cos^2 x -8cos^2 x +1

Answer 2

4cos^{2}2x-1=cos4x