question

*To*: mathgroup at smc.vnet.net*Subject*: [mg77827] question*From*: dimitris <dimmechan at yahoo.com>*Date*: Sun, 17 Jun 2007 06:21:19 -0400 (EDT)

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

**Follow-Ups**:**Re: question***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: question***From:*Carl Woll <carlw@wolfram.com>