Chapter 7.7, Problem 13P

If $f(x)=\frac{1}{2}{a}_0+{\displaystyle \underset{1}{\overset{\infty }{\sum }}{a}_n}\cos nx+{\displaystyle \underset{1}{\overset{\infty }{\sum }}{b}_n}\sin nx={\displaystyle \underset{-\infty }{\overset{\infty }{\sum }}{c}_n}{e}^{inx},$ use Euler’s formula to find $a_n$ and $b_n$ in terms of $c_n$ and $c_{-n},$ and to find $c_n$ and $c_{-n}$ in terms of $a_n$ and $b_n$ a.