• To: mathgroup at smc.vnet.net
• Subject: [mg104450] Re: Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sun, 1 Nov 2009 03:57:38 -0500 (EST)

```On 10/30/09 at 2:19 AM, lawrenceteo at yahoo.com (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.

When you did the subtraction did you do:

In[5]:= Cos[x]^2 - Sin[x]^2 - (Cos[x]^4 - Sin[x]^4) // Simplify

Out[5]= 0

which is correct. Or did you fail to include the parentheses and do

In[6]:= Cos[x]^2 - Sin[x]^2 - Cos[x]^4 - Sin[x]^4 // Simplify

Out[6]= -2 sin^4(x)

Since, this result could be characterized as a "small delta", my
guess is this is what you did. But this is not the difference
between the two expressions.

```

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