Sigma Notation Question/Trig Identity

  • Thread starter Lamoid
  • Start date
  • #1
44
0
[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?
 

Attachments

  • question2.jpg
    question2.jpg
    8 KB · Views: 454

Answers and Replies

  • #2
1,631
4
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]
 
  • #3
44
0
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:
  • #4
1,631
4
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?

[tex] A=(n+\frac{1}{2})x[/tex]

[tex]B=\frac{x}{2}[/tex]
 
  • #5
Gib Z
Homework Helper
3,346
6
It is a "Sum to product identity".
 

Related Threads on Sigma Notation Question/Trig Identity

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
21
Views
7K
  • Last Post
Replies
2
Views
6K
  • Last Post
3
Replies
69
Views
12K
  • Last Post
Replies
4
Views
2K
Top