Answer :

The given expression can be rearranged as:


(Cos 1 + cos 179) + (cos2 + cos 178) + (cos3+ cos177) +…. + (cos89 + cos 91) + (cos90) + cos180


We know that: cos(180 - x)= - cos x.


So all the bracket totals except last 2 terms will be zero.


So given expression is: 0 + (cos90) + ( cos180)


= 0 + 0 + (-1)


=-1.


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