Q. 12

# Write the value of cos 1° + cos 2° + cos 3° + ... + cos 180°.

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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