simplifying expressions – How to prevent TrigReduce auto evaluating Sin and Cos

Mathematica automatically evaluates Sin and Cos when TrigReduce is applied. For example, TrigReduce(Cos(2*t)*Cos(2*t)) results in 1/2 (1 + Cos(4 t)). In my application I would like TrigReduce to keep the Sin and Cos as is. I’d like to have 1/2 (Cos(0 t) + Cos(4 t)) as the output of the preceding example. I tried to use Inactivate, but that seems to prevent TrigReduce from working as well.