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

• To: mathgroup at smc.vnet.net
• Subject: [mg104413] Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: David Reiss <dbreiss at gmail.com>
• Date: Sat, 31 Oct 2009 01:49:45 -0500 (EST)
• References: <hce437$r4t$1@smc.vnet.net>

Because

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

and

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

--David

On Oct 30, 3:20 am, Lawrence Teo <lawrence... 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.