The following command does what I want:
TrigExpand[ Cos[a + b]^2] (* 1/2 + 1/2 Cos[a]^2 Cos[b]^2 - 1/2 Cos[b]^2 Sin[a]^2 - 2 Cos[a] Cos[b] Sin[a] Sin[b] - 1/2 Cos[a]^2 Sin[b]^2 + 1/2 Sin[a]^2 Sin[b]^2 *)
Unfortunately, it does not apply the distributive property of the product in another case, that is the one I am interested in:
TrigExpand[ Cos[c*(a + b)]^2] (* Cos[c*(a + b)]^2 *)
How can I tell Mathematica to do that initial step?