Taylor Polynomial for f(x)=sec(x)

[ehilge]

Hey all, so I need to find 4th degree taylor polynomial of f(x)=sec(x) centered at c=0

Can I just use substitution to find the answer since sec(x) = 1/cos(x) and I know the taylor series for cos(x). I guess, essentially, can I take the reciprocal of the taylor series of cosx to get sec(x). (in the same way for sin ((x^3)) you can just plug in x^3 wherever there is an x in the taylor series)

I know if this doesn't work I can keep taking the derivatives of secx and plug everything in and expand it out and all of that jazz. I did start to take the derivatives of sec(x) before I realized that it got excessively complicated and cumbersome.

So if my original idea doesn't work, what would be a better way to solve the problem without having to differentiate a whole bunch?

Thanks!

 

[Hurkyl]

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