Question

вычислить:cos(пи/5)+cos(2пи/5)+cos(4пи/5)+cos(6пи/5)

Answer 1

 
 $cos(frac{pi}{5}) + cos(frac{2pi}{5}) + cos(frac{4pi}{5})+cos(frac{6pi}{5})=\\ 2cosfrac{7pi}{10}*cosfrac{pi}{2} +cosfrac{2pi}{5}+cosfrac{4pi}{5}=\\ frac{2sinfrac{2pi}{5} (cosfrac{2pi}{5}+cosfrac{4pi}{5})}{2sinfrac{2pi}{5}} =\\ sinfrac{4pi}{5}+sinfrac{6pi}{5}-sinfrac{2pi}{5} = -sinfrac{2pi}{5}\\ frac{-sinfrac{2pi}{5}}{2sinfrac{2pi}{5}} = - frac{1}{2}$