cos 1° + cos 2° + cos 3° + ........ + cos180° is equal to __________.

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answer is D.

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Detailed Solution

Given, cos 1° + cos 2° + cos 3° + ........ + cos 180°
= (cos 1° + cos 179°) + (cos 2° + cos 178°) + ........ + (cos 89° + cos 91°) + cos 90° + cos 180o
= [cos 1° + cos (180° – 1°)] + [cos 2° + cos (180° – 2°)] +....... + [cos 89° + cos (180° – 91°)] + cos 90° + cos 180°
= (cos 1° – cos 1°) + (cos 2° – cos 2°) +....... + (cos 89° – cos + 89°) + 0 + (– 1) = – 1.
(As, cos (180° – θ) = – cos θ)

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