fourth trig question from one billion

The answer is "A"= -1

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

Thanks CPhill !