As part of my final year project, I'm using the identity $\displaystyle cos(z sin \theta ) = J_{0} (z) + 2 \sum _{k=1}^{oo} J_{2k} (z) cos (2k \theta )$ where J is a Bessel function of the first kind.

Instead of just quoting this, it would be quite nice to actually prove it, so I was wondering if anyone could direct me in how to do so?