Question

Use DeMoivre's formula to write cos(6X) in terms of sin(x) and cos(x)

Answer 1

\[\Large \cos\alpha+i\sin\alpha=e^{i\alpha} \]

De Moivre states that:

\[\Large \left(\cos\alpha+i\sin\alpha \right)^n=\cos(n\alpha)+i\sin(n\alpha) \]

So you can plugin \(n=6\) and then multiply out the binomial progression, compare coefficients afterwards.

Answer 2

To be a bit clearer, compare real and imaginary parts with one another.