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