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


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

				

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