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I have been asked to show that the following is true, and I have been at it now for more time than I care to admit.

Prove that

$\sum_{n = 0}^{N -1} cos(nx) = \frac{sin(Nx/2)}{sin(x/2)} cos(N-1) \frac{x}{2}$

I've done a lot of playing around with identities. I think this one is a little beyond me right this moment. please let's keep this a secret.

I will model the solution of the next one

$\sum_{n = 0}^{N -1} sin(nx) = \frac{sin(Nx/2)}{sin(x/2)} sin(N-1) \frac{x}{2}$

Based on input from the first one.

cows
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  • What have you tried? Can you show us some of your attempts? Those may be more along the right track than you realize. – Clayton Aug 27 '22 at 01:17
  • I managed to prove it late last night. I might be uploading a picture of the proof soon. – cows Aug 28 '22 at 00:54

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