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

*To*: mathgroup at smc.vnet.net*Subject*: [mg104409] Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?*From*: pratip <pratip.chakraborty at gmail.com>*Date*: Sat, 31 Oct 2009 01:49:00 -0500 (EST)*References*: <hce437$r4t$1@smc.vnet.net>

On Oct 30, 8:20 am, Lawrence Teo <lawrence... 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. Hi, Please remember the basic identity Cos[x]^2+Sin[x]^2=1 (* We multiply both sides of the equation with (Cos[x]^2-Sin[x]^2) *) =>(Cos[x]^2+Sin[x]^2)*(Cos[x]^2-Sin[x]^2)=1*(Cos[x]^2-Sin[x] ^2) (* remember (a+b)(a-b)=a^2-b^2 *) =>(Cos[x]^4-Sin[x]^4)=Cos[2x] Also for this type of doubt one can take help of the Plot function in Mathematica. Plot[Evaluate[{Cos[x]^4 - Sin[x]^4, Cos[2 x], Cos[x]^2 - Sin[x]^2}], {x, -2 Pi, 2 Pi}, PlotStyle -> {{Red}, {Blue, Dashed}, {Cyan}}] You will see all the three functions that we are plotting will coincide. Hope this helps you. Regards, Pratip