Question

how do I figure out that csc^2x*sinx-cotx*sinx*tanx=cosx*cotx

Answer 1

\(\bf csc^2(x)sin(x)-cot(x)sin(x)tan(x)=cos(x)cot(x)
\\ \quad \\
\implies \cfrac{1}{sin^2(x)}\cdot sin(x)-\cfrac{cos(x)}{sin(x)}\cdot sin(x)\cdot \cfrac{sin(x)}{cos(x)}\)

what would that left-side give you?