Stavros comments at this Maxima thread that
The simplification acos(cos(x)) => x is only valid when 0 <= x <= %pi, so
Maxima by default does not perform that simplification. (And unfortunately,
it is not clever enough to perform it when x is declared to be in that
This still seems to be the case - see this ask.sagemath.org question. So... I nominate this as a bug, or at least a candidate for improvement, since asin(sin(x)) does seem to be smart enough.