The given expression is Ctgt(-t)sint + cost(Pi + t).

To simplify, we use trigonometric identities:

cot(-t) = -cot(t)sin(-t) = -sin(t)cos(Pi + t) = -cos(t)

Therefore, the expression becomes:

C(-cot(t))(sin(t)) + (-cos(t))

Which simplifies to:

-Ccot(t)sin(t) - cos(t)

So, Ctgt(-t)sint + cost(Pi + t) simplifies to -Ccot(t)sin(t) - cos(t).