I'll make my self more clear.
Suppose you were to find, the FS of f(t)= cos(t) for 0<t<pi and f(t)=0 -pi<t<0
We would get FS(t) = 1/2 Cos(t) + Sigma 2/pi (n/n^2-1) for n = even
Now how on earth do I get 1/2 cos(t) from my Integeral coefficients?
My A0 =0 An=0 but Bn= Sigma .....
Unless I say, 1/2 cos(t) must be there due to the fact that at t=0 I must get f(t) = 1/2 ???? which follows from Dirichlets Theorem ?