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Homework Help: Sigma Notation Question/Trig Identity

  1. Mar 5, 2008 #1
    [SOLVED] Sigma Notation Question/Trig Identity

    I posted this elsewhere but I think I put it in the wrong place so I'm gonna 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?
     

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  2. jcsd
  3. Mar 5, 2008 #2
    i do not think those formulas are correctly written, i mean the second one. the last part should read like this i guess:

    [tex]\frac{sin(\frac{nx}{2})cos(\frac{1}{2}(n+1)x)}{sin\frac{x}{2}}[/tex]

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

    [tex]sin(A)-sin(B)=2cos(\frac{A+B}{2})sin(\frac{A-B}{2})[/tex]
     
  4. Mar 5, 2008 #3
    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?
     
    Last edited: Mar 5, 2008
  5. Mar 5, 2008 #4
    [tex] A=(n+\frac{1}{2})x[/tex]

    [tex]B=\frac{x}{2}[/tex]
     
  6. Mar 6, 2008 #5

    Gib Z

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    Homework Helper

    It is a "Sum to product identity".
     
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