$\tan{3\theta} \,=\, \dfrac{3\tan{\theta}-\tan^3{\theta}}{1-3\tan^2{\theta}}$
$\dfrac{3\tan{\theta}-\tan^3{\theta}}{1-3\tan^2{\theta}} \,=\, \tan{3\theta}$
It is called tan triple angle identity and used in two cases as a formula.
The tangent of triple angle identity is used to either expand or simplify the triple angle tan functions like $\tan{3A}$, $\tan{3x}$, $\tan{3\alpha}$ and etc. For example,
$(1) \,\,\,\,\,\,$ $\tan{3x} \,=\, \dfrac{3\tan{x}-\tan^3{x}}{1-3\tan^2{x}}$
$(2) \,\,\,\,\,\,$ $\tan{3A} \,=\, \dfrac{3\tan{A}-\tan^3{A}}{1-3\tan^2{A}}$
$(3) \,\,\,\,\,\,$ $\tan{3\alpha} \,=\, \dfrac{3\tan{\alpha}-\tan^3{\alpha}}{1-3\tan^2{\alpha}}$
Learn how to derive the rule of tan triple angle identity by geometry in trigonometry.
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the maths problems in different methods with understandable steps.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved