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

• To: mathgroup at smc.vnet.net
• Subject: [mg104414] Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Sat, 31 Oct 2009 01:49:56 -0500 (EST)
• References: <hce437\$r4t\$1@smc.vnet.net>

```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.
>
it's simply true, because:

cos^4 x - sin^4 x = (cos^2 x - sin^2 x)(cos^2 x + sin^2 x)
= (cos^2 x - sin^2 x) * 1 = cos 2x

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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