# [seqfan] Re: Two roots of trigonometric polynomials

Charles Greathouse charles.greathouse at case.edu
Wed Oct 2 21:43:11 CEST 2013

```Zero[aa_] :=
With[{a = Exp[2 I*TrigToExp[aa]]},
FullSimplify[Numerator[a] - Denominator[a]] == 0]

Zero[(x /.
Solve[Cos[6 x] == Cos[4 x]^2 && 0 < x < 1, x,
Reals][[1]][[1]]) - (x /.
Solve[Cos[x]^2 + Sin[3 x]^2 == 1/2 && 0 < x < 1, x,
Reals][[1]][[1]])]

True

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Wed, Oct 2, 2013 at 2:44 PM, Robert G. Wilson v <rgwv at rgwv.com> wrote:

> I also "Played" with Mathematica. I first looked that their graphs from 0
> to
> Pi. Bob.
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Charles
> Greathouse
> Sent: Wednesday, October 02, 2013 2:21 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: Two roots of trigonometric polynomials
>
> I was able to prove that the constants are the same by the time-honored
> method of "playing with Mathematica". I don't yet have anything nice, but
> you should be able to recycle A197757 while I look for something more
> presentable.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
>
> On Wed, Oct 2, 2013 at 1:48 PM, Richard J. Mathar
> <mathar at mpia-hd.mpg.de>wrote:
>
> > Is there a way to reduce the trigonometric expressions in
> > http://oeis.org/A197757
> > and http://oeis.org/A197488 to demonstrate that the two constants are
> > the same?
> >
> > RJM
> >
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```