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Re: question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg77848] Re: question
*From*: roland franzius <roland.franzius at uos.de>
*Date*: Mon, 18 Jun 2007 06:58:54 -0400 (EDT)
*Organization*: Universitaet Hannover
*References*: <f5338c$3pc$1@smc.vnet.net>
dimitris wrote:
> Two eforts in Mathematica 5.2 in order
> to simplify o below
>
> o = 2*Cos[Pi/48]*(1 - Cos[Pi/48]^2)^(1/2) + 2*Cos[Pi/48]^2 - 1;
>
> First leaving Mathematica do the job.
>
> Timing[ToRadicals[RootReduce[(FullSimplify[#1, ComplexityFunction ->
> (Count[{#1}, _Cos, Infinity] & )] & )[o]]]]
> {43.031*Second, Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt[3]])]}
>
> Then help a bit Mathematica.
> I couldn't find a built in command to simplify 1 - Cos[Pi/48]^2 to
> Sin[Pi/48]^2. That's why the adding of a rule.
>
> Timing[ToRadicals[RootReduce[Simplify[o /. 1 - Cos[Pi/48]^2 ->
> Sin[Pi/
> 48]^2]]]]
> {0.25*Second, Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt[3]])]}
>
> Any other suggestions will be highly appreciated.
Timing[o // TrigToExp // FullSimplify]
{8.512*Second, (1/2)*Sqrt[4 - Sqrt[2] + Sqrt[6]]}
Timing[o /. Cos[x_] :> 1/Sqrt[1 + Tan[x]^2] // FullSimplify]
{0.631*Second, (1/2)*Sqrt[4 - Sqrt[2] + Sqrt[6]]}
--
Roland Franzius
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