Re: Wrong Simplify Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- To: mathgroup at smc.vnet.net
- Subject: [mg104414] Re: Wrong Simplify Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- From: Peter Breitfeld <phbrf at t-online.de>
- Date: Sat, 31 Oct 2009 01:49:56 -0500 (EST)
- References: <firstname.lastname@example.org>
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. > it's simply true, because: cos^4 x - sin^4 x = (cos^2 x - sin^2 x)(cos^2 x + sin^2 x) = (cos^2 x - sin^2 x) * 1 = cos 2x -- _________________________________________________________________ Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de