Solveit, we need to remember that sin^2 (theta) + cos^2(theta) = 1
So we have :
[sin^4 (theta - cos^2(theta)] / [ cos^2 (theta) - sin^2(theta) ] factor the numerator as a difference of squares, and we have
[ (sin^2 theta + cos^2(theta)] [ sin^2(theta) - cos^2(theta) ] / [ cos^2(theta) - sin^2(theta)]
1 * [ sin^2 (theta) - cos^2(theta)] / [ cos^2 ( theta) - sin^2(theta) ] factor a "-1" out of the numerator
1 * (-1)[cos^2(theta) - sin^2(theta)] / [cos^2(theta) - sin^2 (theta)] =
1 * -1 =
-1