perplexus.info :: Geometry : Sum The Secants, Get 6

Sum The Secants, Get 6 (Posted on 2007-09-12)

Show that:

sec(2π/9) + sec(4π/9) + sec(8π/9) = 6

See The Solution Submitted by K Sengupta

Rating: 2.0000 (1 votes)

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Hint

| Comment 1 of 2

We know that, cos(pi/3) = 1/2, and cos 2x = 2*(cos x)^2 - 1, giving :
cos(2*pi/3) = -1/2, and so:
cos 3h = -1/2
where h = 2*pi/9, 4*pi/9, 8*pi/9

From the relationship between cos 3h and cos h, we will obtain a cubic equation in terms of cosh.

Edited on September 13, 2007, 11:36 am

Posted by K Sengupta on 2007-09-13 03:19:26

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