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


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.


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