There is a function $ f: \mathbb{R}\mathop{\longrightarrow}\mathbb{R} $ which meets the conditions:
$ f(-x)=f(x) $ and $ f(x+ \pi)=-f(x) $ for $ x \in \mathbb {R} $
Show that the Fourier series coefficients are:
$a_{0}=a_{2}=a_{4}=a_{6}=...=0 $ and $b_{1}=b_{2}=b_{3}=b_{4}=...=0$