Sum of Squares of Sine and Cosine/Corollary 1

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

where $\sec$, $\tan$ and $\cos$ are secant, tangent and cosine respectively.

Proof
When $\cos x \ne 0$:

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

or:
 * $\tan^2 x = \sec^2 x - 1 \quad \text {(when $\cos x \ne 0$)}$