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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    
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Some Thoughts Interesting observation | Comment 1 of 8
Using Excel and substituting "N" in place of "13", I note that:
The first term only shows equality for "3".
ie tan(pi/3) = 3^(1/2).

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
  Posted by Larry on 2014-08-17 10:20:09
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