4.21 How to write structured types to match some expressions?

4.21.1 type for \(\sin ^m(x)\cos ^n(x)\)

restart; 
my_type:=''`*`'( { Or('specfunc'(sin),'specfunc'(sin)^Or(integer,rational)), 
                   Or('specfunc'(cos),'specfunc'(cos)^Or(integer,rational))})'; 
 
type(sin(x)^2*cos(x)^3,my_type); 
type(sin(x)^2*cos(x),my_type); 
type(sin(x)*cos(x),my_type); 
type(cos(x)*sin(x)^(1/2),my_type); 
 
 
           true 
           true 
           true 
           true
 

I could not find a way to avoid writing  Or('specfunc'(sin),'specfunc'(sin)^Or(integer,rational) in order to match both \(\sin x\) and \(\sin ^2 x\). For these things, I find Mathematica patterns more flexible. The above can be done as follows in Mathematica

 
ClearAll[x,n,m,any] 
patt=any_.*Sin[_]^n_. * Cos[_]^m_. 
MatchQ[Sin[x]^2*Cos[2*x]^3,patt] 
MatchQ[Sin[x]^2*Cos[x],patt] 
MatchQ[Sin[x]*Cos[x],patt] 
MatchQ[Cos[x]*Sin[x],patt] 
 
      True 
      True 
      True 
      True
 

In Mathematica  n_.  says basically to match \(\sin x\) or \(\sin ^2 x\) since the dot says to match zero or more. So no need to duplicate things as I did above in Maple. There might be a way to do the same in Maple using structured type, but I could not find it. In General, I find patterns in Mathematica more flexible and easier to use for this sort of thing. Maple has patmatch command, but not as easy to use as Patterns in Mathematica.