Possible Duplicate:
Showing that $\sec z = \frac1{\cos z} = 1+ \sum\limits_{k=1}^{\infty} \frac{E_{2k}}{(2k)!}z^{2k}$
Show that $\sec{z}=1+\sum_{k=1}^{\infty}{\frac{E_{2k}}{(2k)!}\,z^{2k}}$ for some constants $E_2, E_4,\ldots$ known as the Euler numbers.
Is there a clever way to do this that doesn't involve taking several derivatives? I thought at first of taking advantage of $\sec{z}=\frac{1}{\cos{z}}$ and using the expansion of cosine, but I'm not sure where to go with it
Thanks