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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[540]= 1
>
> Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2 // FullSimplify
> Out[541]= 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
>

• References:
  • Surprising FullSimplify result
    • From: Sam Takoy <sam.takoy@yahoo.com>