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sin 10+sin 20+..,....................................sin 340+sin 350=?
Solution: i) There are 36 terms; ii) Group them as: (sin10° + sin350°) + (sin20° + sin340°) + (sin30° + sin330°) + .... + .. + (sin170° + sin190°) + (sin180° + sin360°) This forms to 18 pairs. Each pair is zero. sin10° + sin350° = sin10° + sin(360 - 10) = sin10° - sin10° = 0 Like this every pair becomes zero. Thus total sum is zero.
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