Cotangent of Complement equals Tangent

Theorem

 * $\cot \left({\dfrac \pi 2 - \theta}\right) = \tan \theta$ for $\theta \ne \left({2 n + 1}\right) \dfrac \pi 2$

where $\cot$ and $\tan$ are cotangent and tangent respectively.

That is, the tangent of an angle is the cotangent of its complement.

This relation is defined wherever $\cos \theta \ne 0$.

Proof
The above is valid only where $\cos \theta \ne 0$, as otherwise $\dfrac {\sin \theta} {\cos \theta}$ is undefined.

From Cosine of Multiple of Pi Plus Half it follows that this happens when $\theta \ne \left({2 n + 1}\right) \dfrac \pi 2$.