L.H.S = cos 10° + cos 110° + cos 130°
= (cos 10° + cos 110°) cos 130°
= 2 cos (\(\frac{110+10°}{2}\)) cos ( \(\frac{110-10°}{2}\) ) + cos 130°
[∵ cosC + cosD = 2 cos ( \(\frac{C+D}{2}\) ) cos ( \(\frac{C-D}{2}\))]
= 2 cos 60° cos 50° + cos 130°
= 2 × \(\frac{1}{2}\) cos 50° + cos (180° − 50)
= cos 50° - cos 50°
= 0 = R. H.S Hence Proved
