Question #302224

Qn 4. For a given angle θ, suppose that

sin2 θ + cos2 θ = 1 and cos2 θ − sin2 θ = cos 2θ.

2Derive an expression for cos 4θ in terms only of powers of cos θ


1
Expert's answer
2022-02-28T16:36:40-0500
cos2θ=cos2θsin2θ=2cos2θ1\cos 2θ=\cos ^2θ-\sin ^2θ=2\cos^2\theta-1

cos4θ=2cos22θ1=2(2cos2θ1)21\cos 4θ=2\cos^22\theta-1=2(2\cos^2\theta-1)^2-1

=8cos4θ8cos2θ+1=8\cos^4\theta-8\cos^2\theta+1


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