Cotangent of Complement equals Tangent

Theorem

 * $\map \cot {\dfrac \pi 2 - \theta} = \tan \theta$ for $\theta \ne \paren {2 n + 1} \dfrac \pi 2$

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 Half-Integer Multiple of Pi it follows that this happens when $\theta \ne \paren {2 n + 1} \dfrac \pi 2$.

Also see

 * Sine of Complement equals Cosine
 * Cosine of Complement equals Sine
 * Tangent of Complement equals Cotangent
 * Secant of Complement equals Cosecant
 * Cosecant of Complement equals Secant