Let's simplify the given expression step by step.

First, we know that cotangent is the reciprocal of tangent, so we can rewrite ctg(90°+a) as 1/tg(90°+a).

Next, we use the trigonometric identity tg(90°-a) = cot(a), so we can rewrite tg(90°-a) as cot(a).

Now, the expression becomes:

(cot(a) - 1/tg(90°+a))^2

Next, we can combine the fractions under a common denominator:

(cot(a) - 1/tg(90°+a))^2 = ((cot(a)*tg(90°+a) - 1) / tg(90°+a))^2

Since cot(a)*tg(90°+a) = 1, the expression simplifies to:

((1 - 1) / tg(90°+a))^2 = (0 / tg(90°+a))^2 = 0

Therefore, the final answer is 0.