We have to verify if cos^4x + 2sin^2x - sin^4x = 1.

Now cos^4x + 2sin^2x - sin^4x

=> [(cos x)^2]^2 + 2sin^2x - sin^4x

Now use the relation (cos x)^2 = 1 - (sin x)^2

=> [1 - (sin x)^2]^2 + 2sin^2x - sin^4x

Open the brackets

=> 1 + (sin x)^4 - 2( sin x)^2 +2sin^2x - sin^4x

cancel the common terms

=> 1

**Therefore we have proved that cos^4x + 2sin^2x - sin^4x = 1**

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