((ctg(a))^2(((cos(a)) ^2-1

First, we simplify the inner expression:

(cos(a))^2 - 1 = 1 - sin(a)^2 - 1 = -sin(a)^2

Now, replace this into the original expression:

(ctg(a))^2(-sin(a)^2) = (1/tan(a))^2(-sin(a)^2) = (cos(a)/sin(a))^2*(-sin(a)^2)
= (cos(a))^2

Therefore, the simplified expression is: (cos(a))^2