I have to simplify this beam form (equation 1) which simplifies to equation 2 and then finally to equation 3.
equation 1: e^-ix((1-e^y)/(1-e^z)) where x = Beta*M_(1/2), y = beta*M, z= Beta
equation 2: sin(M*Beta/2)/(sin(Beta/2))
equation 3: M((sinc(M*Beta/2pi))/(sinc(Beta/2pi))) where sinc(x) = sin(pi*x)/pi*x
Eulors: e^jx = cos(x) +j*sin(x)
The Attempt at a Solution
I have tries to use eulors equation to change it to sine sand cosine but I cant seem to get the proper cancellations i am looking for.