Question

Express cos(4θ) and sin(4θ) as polynomials in cos(θ),sin(θ).

Answer 1

cos 4θ = 2cos^2 2θ - 1
= 2 (2 cos^2 θ - 1)^2 - 1
= 2( 4 cos^4 θ - 4 cos^2 θ + 1) - 1
= 8 cos^4 θ - 8 cos^2 θ + 1 Answer

sin 4 θ = 2 sin 2θ cos 2θ
= 2 ( 2 sinθ cosθ * (2cos^2θ - 1))
= 2(4 sin θ cos^3θ - 2 sinθ cosθ)
= 8 sin θ cos^3θ - 4 sin θ cos θ