Double Angle Formula for Tangent/Corollary

Theorem
Let $u = \tan \dfrac \theta 2$.

Then:
 * $\tan \theta = \dfrac {2 u} {1 - u^2}$

where $\tan$ denotes tangent.

Proof
From Double Angle Formula for Tangent:


 * $\tan 2 \theta = \dfrac {2 \tan \theta} {1 - \tan^2 \theta}$

The result follows by substituting $\dfrac \theta 2$ for $\theta$.