How do I go about proving that:

Question

cos(4θ) + 4cos(2θ) ≡ 8cos^4(θ) - 3

Thanks in advance!

Answer 1

cos(4θ) = 2cos^2(2θ)-1 = 2(2cos^2(θ)-1)^2-1
4cos(2θ) = 4(2cos^2(θ)-1)
so, add them up