Any help on this would be greatly appreciated! Thank You!
Let $\displaystyle r = 2\theta$, then we have:
$\displaystyle \displaystyle\cos^2{\theta} = \frac{1}{2}\left(1+\cos{r}\right) = \frac{1}{2}\left(1+\sum_{n=0}^{\infty}\frac{(-1)^n(r)^{2n}}{(2n)!}\right)[/Math]
[Math]\displaystyle = \frac{1}{2}+\frac{1}{2}\sum_{n=0}^{\infty}\frac{(-1)^n(r)^{2n}}{(2n)!} = \frac{1}{2}+\frac{1}{2}\sum_{n=0}^{\infty}\frac{(-1)^n(2\theta)^{2n}}{(2n)!} $.