What is cos 20 + cos 40 + ... + cos 160 + cos 180.

 

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We have to determine the value of cos 20 + cos 40 + ... + cos 160 + cos 180

Use the property cos (180 - x) = -cos x

=> cos 20 + cos 40 +... + cos 80 + cos (180 - 80) + cos (180 - 60) +...cos(180 - 20) + cos 180

=> cos 20 + cos 40 +... + cos 80 - cos 80 - cos 60) +... - cos 20) + cos 180

=> cos 180

=> -1

The value of cos 20 + cos 40 + ... + cos 160 + cos 180 = -1.

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