Question Number 32934 by abdo imad last updated on 06/Apr/18
$${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:{prove}\:{that} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} {cos}\left({n}\theta\right)=\:\frac{{xcos}\theta\:−{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{2}{xcos}\theta\:+{x}^{\mathrm{2}} } \\ $$