What is the frequency of $\cos x -\sqrt 2\cos\sqrt 2 x$?
Not sure, whether it's really your question. The signal for which you asked for the frequency actually has two frequencies. There are two components, the two cosines. And each component has a frequency. Assume your frequency is called $f$. So, the signal looks like $\cos(2\pi f x)$. So, getting the frequency of a component is quite easy. Just take everything from it between the brackets and divide it by $2\pi$.

Probably, you already got the frequencies of your signal. But just to be sure, it's: $\frac{1}{2\pi}$ and $\frac{\sqrt{2}}{2\pi}$.

Hope, it was the answer, you're looking for...