       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.
>
> (Count[{#1}, _Cos, Infinity] & )] & )[o]]]]
> {43.031*Second, Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt])]}
>
> 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])]}
>
> Any other suggestions will be highly appreciated.

Timing[o // TrigToExp // FullSimplify]

{8.512*Second, (1/2)*Sqrt[4 - Sqrt + Sqrt]}

Timing[o /. Cos[x_] :> 1/Sqrt[1 + Tan[x]^2] // FullSimplify]

{0.631*Second, (1/2)*Sqrt[4 - Sqrt + Sqrt]}

--

Roland Franzius

```

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