We need to prove the following expression:
[tex]\frac{\csc^2x}{\cot x}=\csc x\sec x[/tex]To do that we need to rewrite the left side of the equation in such a way that it becomes equal to the right side. We have:
[tex]\begin{gathered} \csc x\cdot\frac{\csc x}{\cot x} \\ \csc x\cdot\frac{\frac{1}{\sin x}}{\frac{\cos x}{\sin x}} \\ \csc x\cdot\frac{1}{\sin x}\cdot\frac{\sin x}{\cos x} \\ \csc x\cdot\frac{1}{\cos x} \\ \csc x\cdot\sec x \end{gathered}[/tex]We were able to rewrite the left side of the equation in such a way that it is equal to the right side, so the equation is valid and the identity is verified.
