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

cos(4x) = cos(2(2x)) = 2(cos^2(2x)) - 1 = 2 (cos^2(x) - 1)^2 - 1 = 8(cos^4(x)) - 8(cos^2(x)) + 1