I am trying to prove Parseval's theorem and I have got a problem in this step. So I have shown only a step in this proof. The Fourier coefficient is given by $\displaystyle a_n=\frac{1}{\pi}\int_{-\pi}^{\pi}f(x)cosnx dx$
Now, in this step $\displaystyle \int_{-\pi}^{\pi}a_ncosnxdx$. How should I use the first relation which is fourier coefficient to solve this.