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## Homework Statement

Applications from multiple-slit diffraction involve sums like the following. Prove that:

[tex]\sum^{N-1}_{n=0}[/tex] cos (nx) = [tex]\frac{sin(N(x/2))}{sin(x/2)}[/tex] * cos((N-1)x/2)

## Homework Equations

According to my instructions, this should involve only algebraic manipulations

Also there is this hint:

Use the geometric series formula:

[tex]\sum^{M}_{n=0}[/tex] r[tex]^{n}[/tex]= [tex]\frac{1-r^{M+1}}{1-r}[/tex]

## The Attempt at a Solution

Once again, I apologize for the poor use of Latex. I hope the equation is easily understood. This problem comes from the complex arithmetic section of my book. I originally followed a lot of different trig identity paths until I re-read the part about using only algebraic manipulations.

If possible, I would like a small shove past the hint. I'm not asking for a complete proof here, only a little more light in the right direction. Thanks for taking the time to read.