To simplify the expression, we can first expand the numerator using the difference of squares formula:
cos(2a) - cos^2(a) = cos^2(a) - sin^2(a) - cos^2(a) = -sin^2(a)
Now, we can substitute this back into the original expression:
(-sin^2(a)) / (1 - cos^2(a))
Next, we can use the Pythagorean identity sin^2(a) + cos^2(a) = 1 to simplify the denominator:
(-sin^2(a)) / sin^2(a) = -1
Therefore, the simplified form of the expression is -1.
To simplify the expression, we can first expand the numerator using the difference of squares formula:
cos(2a) - cos^2(a) = cos^2(a) - sin^2(a) - cos^2(a) = -sin^2(a)
Now, we can substitute this back into the original expression:
(-sin^2(a)) / (1 - cos^2(a))
Next, we can use the Pythagorean identity sin^2(a) + cos^2(a) = 1 to simplify the denominator:
(-sin^2(a)) / sin^2(a) = -1
Therefore, the simplified form of the expression is -1.