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 Six tangents (Posted on 2014-08-17)
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

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 re: Interesting observation | Comment 6 of 8 |
(In reply to Interesting observation by Larry)

Using Excel and substituting "N" in place of "13", you did not
ie tan(pi/3) = 3^(1/2)  you have set 2N+1=13
The product of the first 2 terms shows equality for N=5.
The product of the first 3 terms shows equality for N=7.
The product of the first 4 terms shows equality for N=9.
The product of the first 5 terms shows equality for N=11.
The product of the first 6 terms shows equality for N=13.
The product of the first 7 terms shows equality for N=15.

So far, I have no idea why

The product of the first N terms should be = 2N+1

I will try to solve it later, have some ideas but no time now

Edited on August 18, 2014, 10:14 am
 Posted by Ady TZIDON on 2014-08-18 10:01:45

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