@Preben Alsholm Removing filled=true changes nothing. I do like the approach of using trace and multiple plots.

@Carl Love Any idea why for (about) Pi < theta < 5*Pi/4 and 7*Pi/4 < theta < 2*Pi there are regions shown that aren't part of the bounded region?

@Markiyan Hirnyk I apologize if my questions bore you. I did a search and the first few pages of results were not helpful because my search did not include the string "sum difference," or anything closely related. If you are indeed, bored by my queries, please ignore them. I do not think you need to be rude or demeaning because someone asks a question that you deem "unoriginal." Clearly, you have more experience with Maple, and I'm sure you're proud of that. That, however, does not give you the right to treat others with less experience with such disrespect. From what I understand MaplePrimes is designed to provide a forum where ALL users of Maple (and other products) can share and learn.

@Markiyan Hirnyk This solution is sufficient. I can confirm that it, indeed, works. I don't know if it is appropriate to pose another problem that it is closely related to this one, but here goes:

If I change the problem to 2*sin(2*x+Pi/4), and the desired form is sqrt(2)*sin(2*x)+sqrt(2)*cos(2*x), expand(,trig) no longer works for me. How might this one be tackled? Clearly, one may just replace "x" with "2x," but is this the only way?

@Carl Love I knew it had to be something simple. Your explanation is very good!

@Carl Love Yes, I realized that after I posted the question.

@Markiyan Hirnyk This works too, thanks!

@Carl Love This is just what I need. Thanks!

@nm Hence my question. My point is, that answer is not correct. Why is Maple not giving the correct answer?

@spradlig Despite it's convenience, be wary of RealDomain. See http://www.mapleprimes.com/questions/131296-Discrepancy-With-Limit

@spradlig Despite it's convenience, be wary of RealDomain. See http://www.mapleprimes.com/questions/131296-Discrepancy-With-Limit

@Carl Love 

Yes, you are correct. I simply copied and pasted the command from the original question and added explicit. I wouldn't have constructed the command in that manner. :-)

@Carl Love 

Yes, you are correct. I simply copied and pasted the command from the original question and added explicit. I wouldn't have constructed the command in that manner. :-)

Yes, I was able to get the value of 26Pi by manually converting it to cylindrical coordinates. I was wondering if there is a way to prod Maple to do the conversion on its own.

Yes, I was able to get the value of 26Pi by manually converting it to cylindrical coordinates. I was wondering if there is a way to prod Maple to do the conversion on its own.