f(x) = `cos^2 x + cos^2 x = 2 cos^2 x`
Using the trigonometric identities, it can also be stated in different forms,
f(x) = `2 cos^2 x = cos2x + 1 = 2(1-sin^2x)`
Other operations can also be done on it.
f'(x) = `d/(dx) 2 cos^2x = 2 xx2 cosx d/(dx) cos x = 4 cos x (-sinx)`
`= -4 cosxsinx`
Hope this helps.