I have a product of two cosine waves, each with a different period.
$$f(x) = \cos(\omega_1t-\delta)\cos(\omega_2t-\delta)$$
I would like to find the time average of this product using:
$$\frac1T \int_0^T \cos(\omega_1t-\delta)cos(\omega_2t-\delta)dt$$
The period of $f(x)$ is $T = \omega_1\omega_2$, but with this limit, I get a computer solution that seems too complicated to be correct. Is there any reason to believe this integral has a palatable solution? If the integral is analytic, please sketch the method of solution.