sin^2 a +tg(-a) ctg a

Sin^2 a +tg(-a) ctg a = sin²(a) - tg(a)*ctg(a) = sin²(a) - 1 =
= sin²(a) - (sin²(a) + cos²(a)) = sin²(a) - sin²(a) - cos²a = -cos²(a)