Re: question

*To*: mathgroup at smc.vnet.net*Subject*: [mg77851] Re: [mg77827] question*From*: Carl Woll <carlw at wolfram.com>*Date*: Mon, 18 Jun 2007 07:00:27 -0400 (EDT)*References*: <200706171021.GAA02852@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. > >Dimitris > > > Try using Developer`TrigToRadicals: In[2]:= o//Developer`TrigToRadicals//RootReduce//ToRadicals Out[2]= Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt[3]])] Note that I deleted some error messages above that appear in version 5.2, but not in version 6. Carl Woll Wolfram Research

**References**:**question***From:*dimitris <dimmechan@yahoo.com>