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Re: Wrong Simplify[] Answer for

• To: mathgroup at smc.vnet.net
• Subject: [mg104415] Re: [mg104400] Wrong Simplify[] Answer for
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 31 Oct 2009 01:50:07 -0500 (EST)
• Reply-to: hanlonr at cox.net

The only difference is numerical noise, i.e., close to the specifed precision. For example, specifying a precision of 200, the difference is less than 10^-198

Chop[Table[(Cos[x]^2 - Sin[x]^2) -
    (Cos[x]^4 - Sin[x]^4),
   {x, 0, 7, .001`200}], 10^-198] // Union

{0}


Bob Hanlon

---- 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.