Proving that $\cos x \cot^2x$ and $(\csc x \cot x)\cdot(-\cos x)$ are equivalent

Question

I have to prove that $$\cos x \cot^2x \quad\text{and}\quad(\csc x \cot x)\cdot(-\cos x)$$ are equivalent.

When I set $x=10$, and I calculate the result with a scientific calculator, I get the same result.

But how do I prove they are equivalent by using trigonometric properties?

Thank you a lot!

Answer 1

They are not the same. For $0<x<\pi /2$ the first one is positive and second one is negative.