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Question: How can a trigonometric expression, including cos(m*Pi) or sin ((m+1/2)*Pi), be simplified?

Question:How can a trigonometric expression, including cos(m*Pi) or sin ((m+1/2)*Pi), be simplified?

Ali Hassani 120 Maple 2022
simplification trig
April 09 2024
1

 

Dear All,
I want to simplify the following trigonometric expression, considering that m is an integer number. For this, I use the following command:

expr:= 4*cos(Pi*m)/(Pi*(2*m + 1)); 
simplify(%, assume=integer);
factor(%);

However, if I want to simplify the following trigonometric expression, m is an integer number, and alpha is a real number, using the following command will lead to the wrong answer because alpha is also considered an integer number. Please guide me.

4*cos(Pi*m+2*alpha*Pi)/(Pi*(2*m + 1));
simplify(%, assume=integer);
factor(%);

Best wishes
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