How to expand $\cos nx$ with $\cos x$?
Write $\cos(9x)$ in terms of powers of $\cos(x)$
I realize I could solve this by using De Moivre's and binomial expansion:
$\cos(9x) + i \sin(9x) = (\cos(x) + i\sin(x))^9$
then expanding using binomial and extracting the real part of the expansion and using a trig identity to transform any $\sin(x)$ terms.
However, this is going to take some time to do. I was wondering if this was the only way to handle this problem or if there was a more clever way of dealing with such problems, maybe using polar form?