Secant of Right Angle

Theorem

 * $\sec 90^\circ = \sec \dfrac \pi 2$ is undefined

where $\sec$ denotes secant.

Proof
From Secant is Reciprocal of Cosine:
 * $\cot \theta = \dfrac 1 {\cos \theta}$

From Cosine of Full Angle:
 * $\cos \dfrac \pi 2 = 0$

Thus $\cot \theta$ is undefined at this value.