Question: why Maple needed this extra simplify() step here?

Warning: I am newbie in Maplem so if I am missing something obvious, please do not scream at me.

I noticed something strange here. I was trying to simplify this expression to sinh(x). The first step is to convert it to exp() form. Then the next step should have been just another convert to sinh since the resulting exp() expression from the first step was clearly a sinh(). Yet, I find that expand() and also simplify() in order for Maple to see this.

So my question is, what are the rules of the game here? Does one really have to baby step the simplification process like this to the extent of telling Maple that

is the same as

by using simplify(), before getting the result needed?

Here is the code: (the goal again is to obtain sinh(x) as final simplification)

%------ this works --------------
s:=(1/2)*exp((1/2)*x)*(cosh((1/2)*x)-cosh((3/2)*x)+sinh((1/2)*x)+sinh((3/2)*x));
convert(s,exp);
expand(%);
simplify(%);   %-----> without this, will not work
convert(%,sinh);
%--------------------------

but

%---- this does not ----------------
s:=(1/2)*exp((1/2)*x)*(cosh((1/2)*x)-cosh((3/2)*x)+sinh((1/2)*x)+sinh((3/2)*x));
convert(s,exp);
expand(%); 
convert(%,sinh);  % is simplify really needed BEFORE this step?
simplify(%);  % 
----------------------------

Fyi, in Mathematica, I only needed to convert to exp() and back again to Trig to get the answer:

Or using Simplify