The expression provided is sin^2(t) + sin^2(t)*cot^2(t).

Now, we know that cot(t) = 1/tan(t), therefore, cot^2(t) = (1/tan(t))^2 = 1/tan^2(t).

Since cot(t) = cos(t)/sin(t), we can rewrite cot^2(t) as (cos(t)/sin(t))^2 = cos^2(t)/sin^2(t).

So, the expression becomes:

sin^2(t) + sin^2(t)*(cos^2(t)/sin^2(t)) = sin^2(t) + cos^2(t).

By trigonometric identity, sin^2(t) + cos^2(t) = 1.

Therefore, the simplified expression is 1.