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No, how is the form of this 1/2? I know that 1-cosax / ax is 0, but that doesn't seem helpful.

One way or another you need to use the derivative of cos x. Do you know l'Hopital's rule?

or the Taylor/McLauren series of cos x?

Yes, but we haven't gotten to it in class yet, so I'm trying to get there without it.

how about the taylor series of cos x?

No

By algebraically, I meant manipulation not involving derivatives/l'hopital's rule, that is.

(To derive that series, you need to know the derivatives of cos x.)

As ever, you are a gentlemen and a scholar.