Question:

Use De Moivre's Theorem to express $\displaystyle cos6x$ and use the result to solve $\displaystyle 32x^6-48x^4+18x^2=1$.

My problems:

I was under the impression that De Moivre's theorem was something like $\displaystyle (cisx)^n=cisnx$. I don't see how it applies.

My working:

$\displaystyle cos6x = cos^23x - sin^23x$

$\displaystyle cos6x = (16cos^6x + 9cos^2 - 24cos^4x) - (16sin^6x + 9sin^2 - 24sin^4x$

What is this? lol

How do I use DeMoivre's Theorem?