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Question: Infinite summation problem

Question:Infinite summation problem

RLessard 90 Maple 2018
convert sum simplification
February 19 2020
1
Hi !
I have several infinite sommations to evaluate. Maple 2018 on Windows 10 often gives me the solution in terms of hypergeometric functions. I know that the solution can be expressed in terms of sines and cosines.
I am not familiar with sumtools or Sumtools packages.
The convert (expr, StandardFunctions) or simplify (expr, hypergeom) commands do not work.
 
Here is an example of a sommation to evaluate.
 
My old version of Maple V release V (1997 version)  gives me the desired result with the same commands.
 

Is there a command that forces Maple to give me the solution in terms of sines and cosines ?
 
I don't have Mathematica. I hate Mathematica with its difficult syntax but I have access to a computer with Mathematica.
There is a "FunctionExpand" command which converts hypergeometrics into standard functions.
For the previous summation it works very well.
 
Thanks !
Réjean
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