Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- To: mathgroup at smc.vnet.net
- Subject: [mg104427] Re: [mg104400] Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- From: Curtis Osterhoudt <cfo at lanl.gov>
- Date: Sat, 31 Oct 2009 01:52:41 -0500 (EST)
- Organization: LANL
- References: <200910300719.CAA27787@smc.vnet.net>
- Reply-to: cfo at lanl.gov
On Friday 30 October 2009 01:19:47 am 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. > > Cos[x]^2 = 1 - Sin[x]^2 ==> Cos[x]^4 = (1 - Sin[x]^2)^2 = 1 - 2*Sin[x]^2 + Sin[x]^4 = Sin[x]^2 + Cos[x]^2 - 2*Sin[x]^2 + Sin[x]^4 = Cos[x]^2 - Sin[x]^2 + Sin[x]^4 ==> Cos[x]^4 - Sin[x]^4 = Cos[x]^2 - Sin[x]^2 -- ================================== Curtis Osterhoudt cfo at remove_this.lanl.and_this.gov PGP Key ID: 0x4DCA2A10 ==================================
- References:
- Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- From: Lawrence Teo <lawrenceteo@yahoo.com>
- Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?