General Solutions for fMax?

[CH3791]

Hello all,
I am wondering if it is possible to return general solutions for fMax. For example, CASIO Classpad gives {MaxValue=1,x=2π*constn(1)} for fMax(cos(x)). Prime, on the other hand, currently only gives a principal: 0.

Also, in cases when the Prime does provide general solutions, it uses a variable n_integer. You would expect it to be n_1 all the time (or maybe n_2 if there is another solution), but on my calculator at least, n_ is followed by massive integers, sometimes 12, sometimes 120; Once it even got up to 500. The solutions are still correct, but the way n behaves is so weird and annoying.