Question

cos4x = 8 cos^4 x - 8 cos^2 x + 1
Please help me prove! :D 

Answer 1

from cos(2x) = 2cos^2(x) -1

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