Hi, I had solved this problem in a very complex and lengthy way and got the same result as what our lecturer says we should get. However, his answer (which skips several steps) is much simpler than what I did, but I don't know how he does the last step.

Here is the problem:

Find the Fourier sine series of on .

Solution:

We know that , so we will only use the imaginary part of

And what I don't understand is how it goes from the result above to the final result below:

I would really appreciate it if someone could tell me how this is done! I have no clue where the in " " and " " come from... Thanks a lot!