Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- To: mathgroup at smc.vnet.net
- Subject: [mg104421] Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Sat, 31 Oct 2009 01:51:26 -0500 (EST)
- References: <hce437$r4t$1@smc.vnet.net>
On 2009.10.30. 8:20, 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.
>
Cos[x]^4 - Sin[x]^4 ==
== (Cos[x]^2 + Sin[x]^2) * (Cos[x]^2 - Sin[x]^2) ==
== 1 * Cos[2x] ==
== Cos[2x]