Secant is Reciprocal of Cosine

Theorem
Let $\theta$ be an angle such that $\cos \theta \ne 0$.

Then:
 * $\sec \theta = \dfrac 1 {\cos \theta}$

where $\sec$ and $\cos$ mean secant and cosine respectively.

Proof
Let a point $P = \left({x, y}\right)$ be placed in a cartesian plane with origin $O$ such that $OP$ forms an angle $\theta$ with the $x$-axis.

Then:

When $\cos \theta = 0$, $\dfrac 1 {\cos \theta}$ is not defined.