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

• To: mathgroup at smc.vnet.net
• Subject: [mg104427] Re: [mg104400] Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: Curtis Osterhoudt <cfo at lanl.gov>
• Date: Sat, 31 Oct 2009 01:52:41 -0500 (EST)
• Organization: LANL
• References: <200910300719.CAA27787@smc.vnet.net>

```On Friday 30 October 2009 01:19:47 am 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.
>
>

Cos[x]^2 = 1 - Sin[x]^2
==>  Cos[x]^4 = (1 - Sin[x]^2)^2
= 1 - 2*Sin[x]^2 + Sin[x]^4
= Sin[x]^2 + Cos[x]^2 - 2*Sin[x]^2 + Sin[x]^4
= Cos[x]^2 - Sin[x]^2 + Sin[x]^4
==> Cos[x]^4 - Sin[x]^4 = Cos[x]^2 - Sin[x]^2

--
==================================
Curtis Osterhoudt
cfo at remove_this.lanl.and_this.gov
PGP Key ID: 0x4DCA2A10
==================================

```

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