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

• To: mathgroup at smc.vnet.net
• Subject: [mg104440] Re: [mg104400] Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Sat, 31 Oct 2009 01:55:08 -0500 (EST)
• References: <200910300719.CAA27787@smc.vnet.net>

Hi Lawrence,

Well, look:

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

But Cos[x]^2+Sin[x]^2 == 1

Regards,
Leonid


On Fri, Oct 30, 2009 at 10:19 AM, Lawrence Teo <lawrenceteo at yahoo.com>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.
>
>

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