Question

Csc²x/cot x =CSC X sec XI need to verify the identity and I need help knowing how

Answer 1

We need to prove the following expression:

`(\csc^2x)/(\cot x)=\csc x\sec x`

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:

`\begin{gathered} \csc x\cdot(\csc x)/(\cot x) \\ \csc x\cdot((1)/(\sin x))/((\cos x)/(\sin x)) \\ \csc x\cdot(1)/(\sin x)\cdot(\sin x)/(\cos x) \\ \csc x\cdot(1)/(\cos x) \\ \csc x\cdot\sec x \end{gathered}`

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.