Here is the problem:

Find the Fourier coefficients for the discrete-time periodic waveform described below.The waveform has period N = 10; starting at time zero, the waveform values over oneperiod are given by

x[n] = u[n] − u[n − 5]

Below is the solution we were provided by our professor

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My answer to the problem was (line 4 of the solution). My question is, how/why do they add another step in order to have a sin term in the answer (line 5 of the solution)?

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