I believe this might be a problem with assumptions, but I'm not sure.
In the attached file, I attempt to simplify the expression:
(Abs[ Sin[y] Cos[x] ])^2
where x,y are assumed to be real and some constraints are placed on their possible values. As far as I can tell, there is no reason why the Abs function cannot be done away with, and Mathematica in fact agrees that simply removing it doesn't change anything (using == to test returns true in the attached notebook).
I thought perhaps Simplify and FullSimplify just don't recognize the added instance of Abs to be less simple than removing it, but performing the same exercise with a single trig function happily removes the superfluous Abs function, implying that my perception of simpler does agree with Mathematica's in this case.
I experience the same issue with a variety of trig products, either alone or embedded in more complicated expressions. This and similar problems that seem to indicate mathematica isn't using the assumptions I give it have been giving me headaches for a quite some time, so any insight would be much appreciated.
Attachment: SinCos simplification problem.nb, URL: ,