Question

Упростите выражение:

(cos²a - ctg²a)×sin²a

Answer 1

$(cos^2\alpha - ctg^2\alpha )\cdot sin^2\alpha =(cos^2\alpha -\frac{cos^2\alpha }{sin^2\alpha })\cdot sin^2\alpha =cos^2\alpha \cdot sin^2\alpha -cos^2\alpha =\\\\=cos^2\alpha \cdot (sin^2-1)=cos^2\alpha \cdot (-cos^2\alpha )=-cos^4\alpha$