Question

докажите равенство cos п/5 +cos 3п/5= 1/2

Answer 1

$cosfrac{pi}{5}+cosfrac{3pi}{5}=2cdot cosfrac{frac{pi}{5}+frac{3pi}{5}}{2}cdot cosfrac{frac{pi}{5}-frac{3pi}{5}}{2}=2cdot cosfrac{2pi}{5}cdot cos(-frac{pi}{5})=\\=2cdot cosfrac{2pi}{5}cdot cosfrac{pi}{5}=2cdot frac{sqrt5-1}{4}cdot frac{sqrt5+1}{4}=frac{5-1}{8}=frac{4}{8}=frac{1}{2}$