       Re: Simplifying certain trigonometric expressions

• To: mathgroup at smc.vnet.net
• Subject: [mg121038] Re: Simplifying certain trigonometric expressions
• From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
• Date: Wed, 24 Aug 2011 07:49:54 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j328id\$b4g\$1@smc.vnet.net>

```On Wed, 24 Aug 2011 08:17:33 +0100, SamTakoy <pavelgrinfeld at gmail.com>
wrote:

> Hi,
>
> My Mathematica has no problem with
>
> Assuming[x > 0 && y > 0, Cos[ArcTan[y/x]] // FullSimplify]
>
> yielding x/Sqrt[x^2 + y^2], but can't do anything with
>
> Assuming[x > 0 && y > 0, Cos[2 ArcTan[y/x]] // FullSimplify].
>
> How does one overcome this?
>
> Thanks,
>
> Pavel
>

The result you are most likely looking for here has a larger LeafCount
than the input, so in the view of FullSimplify with the default
ComplexityFunction, the given expression cannot be made any simpler. But
you can get a different result by specifying a ComplexityFunction biased
against trigonometric functions:

Assuming[x > 0 && y > 0,
FullSimplify[
Cos[2 ArcTan[y/x]],
ComplexityFunction -> Function[{expr},
100 Count[expr, _Cos | _ArcTan, {0, Infinity}] + LeafCount[expr]
]
]
]

gives

-1 + (2 x^2)/(x^2 + y^2)

which I think is probably what you wanted.

Best,

O. R.

```

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