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?

hint: $\cos x + \cos (180^{\circ}-x) = 2\cos 90^{\circ}\times \cos(x-90^{\circ}) = 2\times 0 \times \sin x=....?$
