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

• To: mathgroup at smc.vnet.net
• Subject: [mg104410] Re: [mg104400] Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: Pratip Chakraborty <pratip.chakraborty at gmail.com>
• Date: Sat, 31 Oct 2009 01:49:11 -0500 (EST)
• References: <200910300719.CAA27787@smc.vnet.net>

```Hi, Please remember the basic identity Cos[x]^2+Sin[x]^2=1 (* We multiply
both sides of the equation with (Cos[x]^2-Sin[x]^2) *)
=>(Cos[x]^2+Sin[x]^2)*(Cos[x]^2-Sin[x]^2)=1*(Cos[x]^2-Sin[x]^2) (* remember
(a+b)(a-b)=a^2-b^2 *) =>(Cos[x]^4-Sin[x]^4)=Cos[2x] Also for this type of
doubt one can take help of the Plot function in Mathematica.
Plot[Evaluate[{Cos[x]^4 - Sin[x]^4, Cos[2 x], Cos[x]^2 - Sin[x]^2}], {x, -2
Pi, 2 Pi}, PlotStyle -> {{Red}, {Blue, Dashed}, {Cyan}}] You will see all
the three functions that we are plotting will coincide. Hope this helps you.
Regards, Pratip

On Fri, Oct 30, 2009 at 8:19 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.
>
>

```

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