# Sextuple Angle Formula for Tangent

$\tan 6 \theta = \dfrac { 6 \tan \theta - 20 \tan^3 \theta + 6 \tan^5 \theta } { 1 - 15 \tan^2 \theta + 15 \tan^4 \theta - \tan^6 \theta }$
where $\tan$ denotes tangent.
 $\ds \tan 6 \theta$ $=$ $\ds \frac {\sin 6 \theta} {\cos 6 \theta}$ Tangent is Sine divided by Cosine $\ds$ $=$ $\ds \frac {\cos^6 \theta \paren {6 \tan \theta - 20 \tan^3 \theta + 6 \tan^5 \theta} } {\cos 6 \theta }$ Formulation 2/Examples/Sine of Sextuple Angle $\ds$ $=$ $\ds \frac {\cos^6 \theta \paren {6 \tan \theta - 20 \tan^3 \theta + 6 \tan^5 \theta} } {\cos^6 \theta \paren {1 - 15 \tan^2 \theta + 15 \tan^4 \theta - \tan^6 \theta} }$ Formulation 2/Examples/Cosine of Sextuple Angle $\ds$ $=$ $\ds \frac { 6 \tan \theta - 20 \tan^3 \theta + 6 \tan^5 \theta } { 1 - 15 \tan^2 \theta + 15 \tan^4 \theta - \tan^6 \theta }$
$\blacksquare$