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

Home > Just Math
Six tangents (Posted on 2014-08-17) Difficulty: 3 of 5
Show that :

tan(pi/13)*tan(2pi/13)*tan (3pi/13)*tan(4pi/13)*tan(5pi/13)*tan (6pi/13) = 13^1/2.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): Interesting observation | Comment 5 of 8 |
(In reply to re(2): Interesting observation by Larry)

Assuming it's true for all n, then it must be true for some less awkward fraction such as tan(pi/15):

tan(pi/15) tan(2pi/15) tan(3pi/15) tan(4pi/15) tan(5pi/15) tan(6pi/15) tan(7pi/15)

When: tan(pi/15)tan((2pi)/15)tan((4pi)/15)tan((7pi)/15) = 1.

and tan(3pi/15)tan((5pi)/15)tan((6pi)/15) = (5-2*5^(1/2))^(1/2)*3^(1/2)*(5+2*5^(1/2))^(1/2) = 15^(1/2).

So that might be an easier place to start.


Edited on August 18, 2014, 5:32 am
  Posted by broll on 2014-08-18 05:02:01

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

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information