sin 10° + sin 20° + sin 40° + sin 50° - sin 70° - sin 80°
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sin A + sin B = 2 sin ½ (A + B) cos ½ (A − B)
so sin 50 + sin 10 = 2 sin 30 cos 20 = 2 *1/2 sin (90-20) = sin 70
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