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sin 10+sin 20+..,....................................sin 340+sin 350=?

sin 10+sin 20+..,....................................sin 340+sin 350=?

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
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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