- #1

earthloop

- 25

- 0

## Homework Statement

[/B]

Hi, I am currently working through a textbook, and the following simplification is given for an example question:

I can't seem to work out how they have moved from cos(pi+n*pi) to cos(pi)cos(n*pi) so easily? Is there a simple trick I have missed? I understand the identity that separates out the sine and cosine terms (-cos(a+b) = sin(a)sin(b)-cos(a)cos(b)) but I'm having very little luck in getting the textbooks answer from that.

2. Homework Equations

2. Homework Equations

cos(a+b) = cos(a)cos(b)-sin(a)sin(b)

cos(a-b) = cos(a)cos(b)+sin(a)sin(b)

-cos(a+b) = sin(a)sin(b)-cos(a)cos(b)

-cos(a-b) = -sin(a)sin(b)-cos(a)cos(b)

## The Attempt at a Solution

applying the identity to the cosine/sine part of the equation ONLY (ignoring 2/(1-n^2) )

**where a = pi**:

[itex]

-\frac{\left(n + 1\right)\, \left(\cos\!\left(a\, n\right)\, \cos\!\left(a\right) + \sin\!\left(a\, n\right)\, \sin\!\left(a\right)\right) + \left(n - 1\right)\, \left(\cos\!\left(a\, n\right)\, \cos\!\left(a\right) - \sin\!\left(a\, n\right)\, \sin\!\left(n\right)\right)}{n^2 - 1}

[/itex]

Am I on the right track?

Thanks