Nyquist Sampling rate
You can use the power reduction formula

$$\cos^2(\theta) = \frac{1 + \cos(2\theta)}{2} $$

on the \$\cos^2(\cdot)\$ term. You'll still have a \$\cos(\theta)\cos(\phi)\$ term but you can use the product-to-sum formula

$$\cos(\theta)\cos(\phi) = \frac{\cos(\theta - \phi) + \cos(\theta + \phi)}{2}$$

to convert it to a sum. That will give you a sum of cosines from which you can pick out the highest frequency.