Sigma Notation Question/Trig Identity

[Lamoid]

[SOLVED] Sigma Notation Question/Trig Identity

I posted this elsewhere but I think I put it in the wrong place so I'm going to post my question again here.


Basically I have to deduce the second formula from the first. Both equations are the same except for the top of the right side, which makes me think it is just a simple matter of a trig identity. Unfortunately, I can't find an identity that would work. Can anyone help?

 

[sutupidmath]

i do not think those formulas are correctly written, i mean the second one. the last part should read like this i guess:

$$\frac{sin(\frac{nx}{2})cos(\frac{1}{2}(n+1)x)}{sin\frac{x}{2}}$$

to deduce this one from the first one, you need to apply this rule

$$sin(A)-sin(B)=2cos(\frac{A+B}{2})sin(\frac{A-B}{2})$$

 

[Lamoid]

OK, but looking at the first formula, wouldn't A be nx? and B be x/2?

Edit: Ah nvm. OK thank you very much! What is that formula called?

 

[sutupidmath]

OK, but looking at the first formula, wouldn't A be nx? and B be x/2?

Edit: Ah nvm. OK thank you very much! What is that formula called?

$$A=(n+\frac{1}{2})x$$

$$B=\frac{x}{2}$$

 

[Gib Z]

It is a "Sum to product identity".