Triple Angle Formulas/Tangent/Proof 3

Theorem

$\tan 3 \theta = \dfrac {3 \tan \theta - \tan^3 \theta} {1 - 3 \tan^2 \theta}$

Proof

From Tangent of Sum of Three Angles:

$\map \tan {A + B + C} = \dfrac {\tan A + \tan B + \tan C - \tan A \tan B \tan C} {1 - \tan B \tan C - \tan C \tan A - \tan A \tan B}$

The result follows by setting $\theta = A = B = C$.

$\blacksquare$