.
At .
Differentiate both sides
At .
Differentiate both sides
At .
Keep going like this until you have the required number of terms.
The question
Find the first three non-zero terms of the Taylor series for sec(z) about 0.
My attempt
Radius of convergence depends on the zeros of cos(z), so
Now, I'm not sure how to proceed. I know the series for cos(z), but I'm not sure how to use it in this context. Any advice?