This equation is incorrect. The correct identity should be:

sin^4x + cos^4x = (sin^2x + cos^2x)^2 - 2sin^2x*cos^2x

When simplifying, we get:

sin^4x + cos^4x = 1 - 2sin^2x*cos^2x

So, the correct identity is:

sin^4x + cos^4x = 1 - 2sin^2x*cos^2x