Find a formula for the first harmonic

The procedure. We have a time-series (N last terms) x(1:N). Find Discrete Fourier Transfom h(1:N) = DFT(x). Find the Inverse DFT for the first harmonic (h(2) and h(N)) y(1:N). How to find a formula for the last term y(N)? I use the Symbolic Math TB:

syms N n x(n) k
h_term(n) = x(n) * exp(-2i*pi*(k-1)*(n-1)/N);
h(k) = symsum(h_term,n,1,N);
%h(2)
%h(N)

%y_term(k) = h(k) * exp(2i*pi*(k-1)*(n-1)/N);
yLast = (h(2) * exp(2i*pi*(N-1)/N) + h(N) * exp(2i*pi*(N-1)*(N-1)/N)) / N;

The formula contains i(=sqrt(-1)) but signals x and y are real. I need a simple formula for programming in C++ without complex numbers and expressions. How to find a simple formula with only sin & cos?