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

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fiona1112 | Student, Grade 11 | eNotes Newbie

Posted November 9, 2011 at 11:04 PM via web

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

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted November 9, 2011 at 11:43 PM (Answer #2)

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You are only allowed one question at a time. The appropriate edit has been made.

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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