Prove that cos8θ=1-32sin^2θ+160sin^4θ-256sin^6θ+128sin^8θ

128sin^8θ

Best way to deal with the expansion is

De Moivre's Theorem

(Cosx + isinx)^n = cosnx + isinnx

Now expand the left hand side using binomial theorem (set n = 8) and ten compare real and imaginary coefficients.

Your Answer Is Ready.

Regards
Anurag