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Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?

• To: mathgroup at smc.vnet.net
• Subject: [mg104407] Re: [mg104400] Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 31 Oct 2009 01:48:38 -0500 (EST)
• References: <200910300719.CAA27787@smc.vnet.net>

On 30 Oct 2009, at 16:19, Lawrence Teo wrote:

> We know that Simplify[Cos[x]^2-Sin[x]^2] -> Cos[2 x]
> But why Simplify[Cos[x]^4-Sin[x]^4] -> Cos[2 x] too?
>
> Doing subtraction between the two expressions will give small delta.
> This is enough to prove that the two expression shouldn't be the same.
>
> Can anyone give me any insight? Thanks.
>

Easy.

Cos[x]^4-Sin[x]^4 == (Cos[x]^2-Sin[x]^2])*(Cos[x]^2+Sin[x]^2])  
(elementery algebra) ==

Cos[x]^2-Sin[x]^2])*1         (elemantary trigonometry)

= Cos[x]^2-Sin[x]^2]) = Cos[2x]

Where did you get your "small delta" from? And can you really imagine  
that a bug like this would hav esurvived nearly two decades of  
Mathematica's existence?

Andrzej Kozlowski

• References:
  • Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
    • From: Lawrence Teo <lawrenceteo@yahoo.com>