All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Sum The Secants, Get 6 (Posted on 2007-09-12) Difficulty: 2 of 5
Show that:

sec(2π/9) + sec(4π/9) + sec(8π/9) = 6

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips 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

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information