Let's simplify the given expression step by step:

Simplify the terms inside the trigonometric functions:
ctg^2(a+pi/2) = 1/tan^2(a+pi/2) = 1/cot^2(a) = cos^2(a)/sin^2(a)
cos^2(a-pi/2) = cos^2(a)

Substitute the simplified terms back into the expression:
(cos^2(a)/sin^2(a)) * cos^2(a)/(cos^2(a) - cos^2(a)) - cos^2(a)

Further simplify the expression:
(cos^4(a)/(sin^2(a)(cos^2(a) - cos^2(a))) - cos^2(a)
(cos^4(a)/(sin^2(a)sin^2(a))) - cos^2(a)
cos^4(a)/(sin^4(a)) - cos^2(a)

Therefore, the simplified form of the given expression is: cos^4(a)/(sin^4(a)) - cos^2(a)