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Trigonometric Fun (Posted on 2004-12-06) Difficulty: 4 of 5
Show that cos(π/7) - cos(2π/7) + cos(3π/7) = 1/2.

See The Solution Submitted by SilverKnight    
Rating: 3.6667 (3 votes)

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re: Solution | Comment 4 of 7 |
(In reply to Solution by Nick Hobson)

Very clever.

I had difficulty understanding the part about the coefficient of z^6.  However, I understand this step better by considering the seven seventh roots of -1 as vectors on the Argand plane, pulling in equal amounts at regular angular intervals, with the net total force then being zero.

  Posted by Charlie on 2004-12-06 21:50:53
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