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Sin10+sin20+sin30+sin 40+sin 50...................................+sin360=?

Sin10+sin20+sin30+sin 40+sin 50...................................+sin360=?

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
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.
 
Regards
Arun (askIITians forum expert)

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