If x(t) is even, then $x(t) = a_0 + \sum_{n=1}^{\infty}a_n*\cos(2\pi nt/T)$
However, based on this formula: $x(t) = a_0 + \sum_{n=1}^{\infty}a_n*\cos(2\pi nt/T) + b_n*\sin(2\pi nt/T)$ where $a_n = 2/T \int_o^Tx(t)*\cos(2\pi nt/T)$
x(t) is an even function and cos is an odd function. An even * odd = odd function. The periodic integral of an odd function is 0. Hence, it should only be the sin term remaining. However, the Fourier Series for these even and odd functions are reversed. It should be that the fourier series of an odd function is the Fourier cosine series. I don't understand.