Sum of Squares of Sine and Cosine/Corollary 2

Corollary to Sum of Squares of Sine and Cosine
For all $x \in \C$:
 * $\csc^2 x - \cot^2 x = 1 \quad \text{(when $\sin x \ne 0$)}$

where $\csc$, $\cot$ and $\sin$ are cosecant, cotangent and sine respectively.

Proof
When $\sin x \ne 0$:

Also defined as
This result can also be reported as:
 * $\csc^2 x = 1 + \cot^2 x \quad \text{(when $\sin x \ne 0$)}$

or:
 * $\cot^2 x = \csc^2 x - 1 \quad \text{(when $\sin x \ne 0$)}$