Derivative of Cosecant Function/Proof 1

Proof
From the definition of the cosecant function:
 * $\csc x = \dfrac 1 {\sin x}$

From Derivative of Sine Function:
 * $\map {\dfrac \d {\d x} } {\sin x} = \cos x$

Then:

This is valid only when $\sin x \ne 0$.