To simplify the expressions provided:

Start with the expression sin^2(a)(1+cot(a)) + cos^2(a)(1+tan(a)) - sin(a)

Using the Pythagorean identities sin^2(a) + cos^2(a) = 1 and cot(a) = 1/tan(a), the expression simplifies to:

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

Next, simplify the expression cot^2(a) - cos^2(a) - cot^2(a)*cos^2(a)

Using the Pythagorean identities cot^2(a) = 1/tan^2(a) and cos^2(a) = 1- sin^2(a), the expression simplifies to:

1/tan^2(a) - (1 - sin^2(a)) - 1/tan^2(a) * (1 - sin^2(a))
= 1/(tan^2(a)) - 1 + sin^2(a) - (1/tan^2(a) - sin^2(a)/tan^2(a))
= 1/(tan^2(a)) - 1 + sin^2(a) - (cot^2(a) - sin^2(a))
= 1/(tan^2(a)) - 1 + sin^2(a) - (1/tan^2(a) - sin^2(a))

Simplify further by expanding and canceling terms, which ultimately yields:

cos^2(a)