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Question

Question: \[\cos 1{^\circ} + \cos 2{^\circ} + \cos 3{^\circ} + ..... + \cos 180{^\circ} =\]...

cos⁡1∘+cos⁡2∘+cos⁡3∘+.....+cos⁡180∘=\cos 1{^\circ} + \cos 2{^\circ} + \cos 3{^\circ} + ..... + \cos 180{^\circ} =

A

0

B

1

C

– 1

D

2

Answer

– 1

Explanation

Solution

(cos⁡1∘+cos⁡179∘)+(cos⁡2∘+cos⁡178∘)+....(\cos 1{^\circ} + \cos 179{^\circ}) + (\cos 2{^\circ} + \cos 178{^\circ}) + ....

+(cos⁡89∘+cos⁡91∘)+cos⁡90∘+cos⁡180∘=−1+ (\cos 89{^\circ} + \cos 91{^\circ}) + \cos 90{^\circ} + \cos 180{^\circ} = - 1.