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

 Submitted by SilverKnight Rating: 3.6667 (3 votes) Solution: (Hide) Subtracting the identities sin( x + y ) = sin(x) cos (y) + cos(x) sin(y),and sin(x-y) = sin(x) cos(y) - cos(x) sin(y) gives us the identity:   2cos(x)sin(y) = sin(x+y) - sin(x-y). So, we have:   2cos(p/7)sin(p/7)=sin(2p/7)-sin(0)   2cos(3p/7)sin(p/7)=sin(4p/7)-sin(2p/7) 2cos(5p/7)sin(p/7)=sin(6p/7)-sin(4p/7) Adding these three equations gives:   2sin(p/7)[cos(p/7) + cos(3p/7) + cos(5p/7)] = sin(6p/7), which gives the result.

 Subject Author Date Solution K Sengupta 2007-05-28 13:33:23 I dont know why? Pemmadu Raghu Ramaiah 2005-01-24 19:36:11 re(2): Arbitrary Evaluation CeeAnne 2004-12-06 23:34:53 re: Solution Charlie 2004-12-06 21:50:53 re: Arbitrary Evaluation Charlie 2004-12-06 21:34:51 Arbitrary Evaluation CeeAnne 2004-12-06 21:20:43 Solution Nick Hobson 2004-12-06 21:10:32

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