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

*To*: mathgroup at smc.vnet.net*Subject*: [mg104407] Re: [mg104400] Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 31 Oct 2009 01:48:38 -0500 (EST)*References*: <200910300719.CAA27787@smc.vnet.net>

On 30 Oct 2009, at 16:19, 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. > > Can anyone give me any insight? Thanks. > Easy. Cos[x]^4-Sin[x]^4 == (Cos[x]^2-Sin[x]^2])*(Cos[x]^2+Sin[x]^2]) (elementery algebra) == Cos[x]^2-Sin[x]^2])*1 (elemantary trigonometry) = Cos[x]^2-Sin[x]^2]) = Cos[2x] Where did you get your "small delta" from? And can you really imagine that a bug like this would hav esurvived nearly two decades of Mathematica's existence? Andrzej Kozlowski

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