Sum of cosines of complementary/suplementary angles Why are $(\cos(2^{\circ})+\cos(178^{\circ})), (\cos(4^{\circ})+\cos(176^{\circ})),.., (\cos(44^{\circ})+\cos(46^{\circ}))$ all equal zero?
Could you prove it by some identity?


so 
  $$cos (2) +cos(178) =cos(2)+cos(180-2)=0\\ cos (4) +cos(176) =cos(4)+cos(180-4)=0\\...\\$$
