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

• To: mathgroup at smc.vnet.net
• Subject: [mg104411] Re: [mg104400] Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
• From: "Tony Harker" <a.harker at ucl.ac.uk>
• Date: Sat, 31 Oct 2009 01:49:22 -0500 (EST)
• References: <200910300719.CAA27787@smc.vnet.net>

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

  Tony Harker

]-> -----Original Message-----
]-> From: Lawrence Teo [mailto:lawrenceteo at yahoo.com] 
]-> Sent: 30 October 2009 07:20
]-> To: mathgroup at smc.vnet.net
]-> Subject: [mg104400] Wrong Simplify[] Answer for 
]-> Simplify[Cos[x]^4-Sin[x]^4]?
]-> 
]-> 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.
]-> 
]-> 

• References:
  • Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
    • From: Lawrence Teo <lawrenceteo@yahoo.com>