Question

Вычислите cos9°+cos18°+cos27°+...+cos162°+cos171°+cos180°​

Answer 1

$\cos 9^\circ+\cos18^\circ+\cos27^\circ+...+\cos 162^\circ+\cos 171^\circ+\cos 180^\circ=\\ \\ =\cos 9^\circ+\cos 18^\circ+\cos 27^\circ+...+\cos (180^\circ-18^\circ)+\cos (180-9^\circ)-1=\\ \\ =\cos 9^\circ+\cos 18^\circ+...-\cos 18^\circ-\cos 9^\circ-1=-1$