Half Angle Formula for Tangent/Corollary 3

Theorem

 * $\tan \dfrac \theta 2 = \csc \theta - \cot \theta$

where $\tan$ denotes tangent, $\csc$ denotes cosecant and $\cot$ denotes cotangent.

When $\theta = k \pi$, the RHS of this formula is undefined.

Proof
When $\theta = k \pi$, both $\cot \theta$ and $\csc \theta$ are undefined.