1. ## Maclaurin Series question

Given

$\frac{1}{1+x^2} = 1 - x^2 + x^4 - x^6...$

$\cos(x) = 1-\frac{1}{2}x^2 + \frac{1}{24}x^4 - \frac{1}{720}x^6 ...$

How would I find the Maclaurin series for $\frac{1}{1+\cos^2(x)}$ ?

I'm pretty sure there's some flaw in my knowledge because I'm not too sure what to do besides let $x = \cos(x)$ which isn't correct.

Could anyone help me out?

2. ## Re: Maclaurin Series question

Why do you think it's not correct, that's exactly what you need to do. Then expand and collect the terms you need up to whatever amount of accuracy you want.