You could go ahead and modify the mathematica output manually by defining exactly what you want to have transformed. In your case this would look like this:
MakeBoxes[Cos[2*x], StandardForm] := RowBox[{MakeBoxes[1 - 2 Sin[x]^2]}]; This effectively turns every occurrence of Cos[2x] in StandardForm into 1 - 2 Sin[x]^2. I use this to get a certain standard notation for dirac delta functions.