Поэтому
cos160°=cos(180°-20°)=-сos 20°;
cos140°=cos(180°-40°)=-сos 40°;
cos120°=cos(180°-60°)=-сos 60°;
cos100°=cos(180°-80°)=-сos 80°.
cos20° + cos40° + cos60° + cos80°+
cos100° + cos120° +cos140° + cos160° + cos180°=
=cos20° + cos40° + cos60° + cos80°-
-cos80°-cos60° -cos40°-cos20°+cos180°= cos180 ° = - 1