Therefore, the simplified expression of (sin^2x - cos^2x)^2 - 4cos^2xsin^2x is 5sin^4x - 2sin^2xcos^2x - 4sin^2x + cos^4x.
It seems that the given result of -0.5 is incorrect based on the simplification we have done. The actual result may be different or there could have been an error in the initial equation.
To simplify the left side of the equation, we will first expand the expression:
(sin^2x - cos^2x)^2 - 4cos^2xsin^2x
(sin^2x - cos^2x)(sin^2x - cos^2x) - 4cos^2xsin^2x
(sin^4x - 2sin^2xcos^2x + cos^4x) - 4cos^2xsin^2x
Next, we will use the trigonometric identity sin^2x + cos^2x = 1 to simplify the expression:
(sin^4x - 2sin^2xcos^2x + cos^4x) - 4cos^2xsin^2x
(sin^4x - 2sin^2xcos^2x + cos^4x) - 4sin^2x(1 - sin^2x)
sin^4x - 2sin^2xcos^2x + cos^4x - 4sin^2x + 4sin^4x
5sin^4x - 2sin^2xcos^2x - 4sin^2x + cos^4x
Therefore, the simplified expression of (sin^2x - cos^2x)^2 - 4cos^2xsin^2x is 5sin^4x - 2sin^2xcos^2x - 4sin^2x + cos^4x.
It seems that the given result of -0.5 is incorrect based on the simplification we have done. The actual result may be different or there could have been an error in the initial equation.