In a networking textbook, I've been given the identity:
$$2\cos^2(2\pi f_ct) = 1 + \cos(4\pi f_ct)$$
I can see that this is just a slight shifting of the double angle identity.
$$\cos(2\theta) = \cos^2 \theta - \sin^2 \theta= 2\cos^2(\theta) - 1$$
But in an example problem, the book shows an output given 2 cosines multiplied with slightly different phases.
$$2\cos(2\pi f_ct)\cos(2\pi f_ct + \phi) = $$
$$\cos(\phi) + \cos(4\pi f_ct + \phi)$$
I don't understand how the last step is made. Is there a more general form of the identity?