Re: How to simplify to a result that is real

• To: mathgroup at smc.vnet.net
• Subject: [mg50821] Re: How to simplify to a result that is real
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 22 Sep 2004 04:51:59 -0400 (EDT)
• Organization: The University of Western Australia
• References: <20040921115025.QQQW18891.lakermmtao10.cox.net@smtp.east.cox.net> <ciqv1p\$ihc\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <ciqv1p\$ihc\$1 at smc.vnet.net>,
Richard Chen <richard at doubleprime.com> wrote:

> Your procedure indeed works. However, the repeated use of
> ComplexExpand with TrigToExp sandwitched in between is hardly
> something people can come up with regularly.
>
> ArcTan[x,y] is indeed different from ArcTan[y/x] in general.
> But the problem is that under our assumptions of a>b>0,0<c<Pi they
> are the same. It is the defect of the current version of mathematica
> not being able to recognize this that is the cause of the problem.
> Otherwise, the relatively simple command
>
> FullSimplify[ComplexExpand[
> Integrate[1/(a + b Cos[t]), {t, 0, c},
> Assumptions -> {a > b > 0, 0 < c < Pi}],
> TargetFunctions -> {Re, Im}], {a > b > 0, 0 < c < Pi}]
>
> will suffice to yield the final concise result.

SetOptions[Integrate, GenerateConditions -> False];

Simplify[Integrate[1/(a + b Cos[t]), {t, 0, c}], a > b > 0]

FullSimplify yields a slightly simpler result in terms of ArcCot instead
of ArcTan.

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
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```

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