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

• To: mathgroup at smc.vnet.net
• Subject: [mg104400] Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: Lawrence Teo <lawrenceteo at yahoo.com>
• Date: Fri, 30 Oct 2009 02:19:47 -0500 (EST)

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.

• Follow-Ups:
  • Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
    • From: Pratip Chakraborty <pratip.chakraborty@gmail.com>
  • Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
    • From: Curtis Osterhoudt <cfo@lanl.gov>
  • Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
    • From: "Tony Harker" <a.harker@ucl.ac.uk>
  • Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
    • From: Leonid Shifrin <lshifr@gmail.com>
  • Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>