       Re: Surprising FullSimplify result

• To: mathgroup at smc.vnet.net
• Subject: [mg111515] Re: Surprising FullSimplify result
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 3 Aug 2010 06:56:54 -0400 (EDT)
• References: <201008021104.HAA27894@smc.vnet.net>

```Well, it looks like Simplify (and FullSimplify) insists on applying
algebraic simplifications before trigonometric ones, that is, I think
that what it does is this:

Simplify[Cos[theta]^2 + Sin[theta]^2 + L^2*Cos[theta]^2,
Trig -> False]

(L^2 + 1)*Cos[theta]^2 + Sin[theta]^2

and only after that it tries to apply trigonometric identities (of
course this is only my hypothesis!). One can force it to return the
desired simplified form by telling it explicitly to leave the third term
alone:

Simplify[Cos[theta]^2 + Sin[theta]^2 + L^2*Cos[theta]^2,
ExcludedForms -> (a_)*Cos[theta]^2]

L^2*Cos[theta]^2 + 1

Andrzej Kozlowski

On 2 Aug 2010, at 13:04, Sam Takoy wrote:

> Here's what I am getting
>
> Cos[theta]^2 + Sin[theta]^2 // FullSimplify
> Out= 1
>
> Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2 // FullSimplify
> Out= 1/2 (2 + L^2 + L^2 Cos[2 theta])
>
> I'm really surprised that the answer in the latter case is not
>
> 1+ L^2 Cos[theta]^2
>
> Is there an explanation?
>
> Thanks,
>
> Sam
>

```

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