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I don’t understand the working

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1 Answer

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After using De Moivre's Theorem, they equal imaginary and real parts (because the equality only holds iff the real and imaginary parts on both parts of the equation of $\cos (4\theta) + i \sin (4 \theta)$ are the same) then $$ Re(\cos (4\theta) +i\sin (4\theta)) = \cos (4\theta) = Re(c^4-6c^2s^2 +s^4+ i(4c^3s-4cs^3) = c^4-6c^2s^2 +s^4$$ then using $\sin (x)^2 = 1 - \cos (x) ^2$ they replace the sinus everywhere and just simplify things.

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