Help with sigma notation problem

[Lamoid]

I have no idea how to use the forum equation code so I just attached the question as a word document. I have no idea how to start this one. Any help is appreciated.

Edit: Ok I just took a screenshot and uploaded it as an image.

 

[Integral]

Many people are rightly relcutant to open .doc files. If you could convert that to PDF format you will find more willing to look at it.

 

[Lamoid]

I think I got it but I would still like for someone to confirm. You use want to find the sum on both sides of the previous identity, so you use telescoping sums on the right side and make it sin ( n+1/2)x - sin (1/2)x. You then divide sin(x/2) from both sides and you prove the formula. Correct?

Also, I am unable to do part b. It looks like I just replace the top of the right side of the formula I proved with a different identity but I can't find one that works.