Typically one would start using the first formula to eliminate all possible products sin(Ax)cos(Ax) and then use the other two on all powers that are left. Roughly speaking, these identities allow us to halve powers in exchange for doubling arguments.
In the end we are left with products of the form f(Ax)g(Bx) with A  B, where the above identities do not help. But we have another set of identities handling exactly this case:

Example: