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

*To*: mathgroup at smc.vnet.net*Subject*: [mg104426] Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?*From*: Helen Read <hpr at together.net>*Date*: Sat, 31 Oct 2009 01:52:29 -0500 (EST)*References*: <hce437$r4t$1@smc.vnet.net>

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. The two expressions are in fact equal. Cos[x]^4 - Sin[x]^4 factors into (Cos[x]^2 + Sin[x]^2)(Cos[x]^2 - Sin[x]^2) and Cos[x]^2 + Sin[x]^2 == 1 (Pythagorean Identity) hence Cos[x]^4 - Sin[x]^4 == Cos[x]^2 - Sin[x]^2 QED -- Helen Read University of Vermont