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.