Re: Trig Fomula

On Thu, 09 Aug 2007 12:29:47 -0500, Robert Israel
<israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

Deep <deepkdeb@xxxxxxxxx> writes:

Any comment and reference about the correctness of the following
assertion will be appreciated.

Assertion: If (1) is valid then (2) is also valid under the given
conditions.

Tan kD = (u/v)^(1/2) (1)

Tan D = (m/n)^(1/2) (2)

Conditions: 0 < D < pi/2; u, v, m, n are integers each > 1 and none is
a pefect square; (u, v) = 1, (m, n) = 1.
Prime k > 3.

Why don't you try a few small examples before making such assertions?

I second this complaint.

However, based on many similar prior posts, I think that Deep probably
lacks the skills and technology to test such conjectures.

In any case, here's a simple counterexample ...

Let u=3,v=2, and let D be the smallest positive real number such that
tan(5D)=sqrt((3/2)). Thus, (1) is satisfied.

It's straightforward to show that tan^2(D) is a root of the equation

2*x^5-115*x^4+520*x^3-530*x^2+110*x-3 = 0

but by the rational root test, the above equation has no rational
roots. Thus (2) fails.

quasi
.

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