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## Homework Statement

How can I calculate it for [tex]\frac{1}{1+cos^2(x)}[/tex] by using the fact that [tex]\frac{1}{1+x^2} = 1 - x^2 + x^4 - ...[/tex]?

## Homework Equations

Given in the problem.

## The Attempt at a Solution

I tried letting u = cos(x), then

[tex]\frac{1}{1+cos^2(x)} = \frac{1}{1+u^2} = 1 - u^2 + u^4 - ... = 1 - cos^2(x) + cos^4(x) - ...[/tex]

But I don't think this is right because the first term should be 0.5, not 1... and I don't see how a -0.5 might pop out of this series of cos terms....and even if it somehow does, I think this question is not meant to be that difficult...

The answer I am trying to get is [tex]\frac{1}{2} + \frac{1}{4}x^2 + ...[/tex]

Any ideas?

Thanks