(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use de Moivre's Theorem to express cos3θ in powers of cosθ

2. Relevant equations

z^n = [r(cosθ + isinθ)]^n = r^n (cos(nθ) + i sin(nθ))

3. The attempt at a solution

cos3θ = Re(cos3θ +isin3θ) = Re[(cosθ +isinθ)^3]

I've then expanded the brackets using binomial theorem and got;

(cosθ)^3 + 3[(cosθ)^2][isinθ] + 3(cosθ)[(isinθ)^2] + (isinθ)^3

So (cosθ)^3 is the real part and 3[(cosθ)^2][isinθ] + 3(cosθ)[(isinθ)^2] + (isinθ)^3 the imaginary part.

If anyone has any suggestions...

Thank you

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# DeMoivre's theorem: cos3θ in powers of cosθ

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