Prove that sums of the form

are equal to sums of the form

*Proof.* We compute this directly, substituting in the formulas for sine and cosine in terms of the complex exponential,

that we derived in this exercise. So, we have

where

Skip to content
#
Stumbling Robot

A Fraction of a Dot
#
Prove that sums of trig functions can be expressed as sums of complex exponentials

###
One comment

### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Prove that sums of the form

are equal to sums of the form

*Proof.* We compute this directly, substituting in the formulas for sine and cosine in terms of the complex exponential,

that we derived in this exercise. So, we have

where

Hi there! Very nice proof! With very minor typo as should be .