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Cos1+cos2+cos3+...cos180=? Please give me the answer

Cos1+cos2+cos3+...cos180=?
Please give me the answer 
 

Grade:10

2 Answers

Arun
25750 Points
4 years ago
Dear student
 
As cos 179 = cos (180-1) = - cos1
Similarly
Cos 178 = - cos2
Cos 177 = - cos3
 
Hencw when adding all terms cancelled out.
Only cos90 + cos180 is remaining
 
Now cos 90 = 0 and cos 180 = - 1
 
Hence final answer is  -1. 
Vikas TU
14149 Points
4 years ago
Dear student 
The given expression can be rearranged as:
(Cos 1 + cos 179) + (cos2 + cos 178) + (cos3+ cos177) +…. + (cos89 + cos 91) + (cos90) + cos180
But we know that: cos(180 - x)= - cos x, where x is angle in degree. So all the bracket totals except last 2 terms will be zero.
So given expression is: 0 + (cos90) + ( cos180)
= 0 + 0 + (-1)
=-1.
Answer: -1.

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