Secant in terms of Tangent

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

where $\sec$ denotes the secant function and $\tan$ denotes the tangent function.

Proof
We also have that:
 * In quadrant I, and quadrant IV, $\sec \theta > 0$
 * In quadrant II, and quadrant III, $\sec \theta < 0$.

When $\cos \theta = 0$, $\tan \theta$ and $\sec \theta$ are undefined.

Also see

 * Trigonometric Functions in terms of each other