# Tan triple angle formula

### Expansion form

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

### Simplified form

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

### Introduction

It is called tan triple angle identity and used in two cases as a formula.

1. Tan of triple angle is expanded as the quotient of subtraction of tan cubed of angle from three times tan of angle by subtraction of three times tan squared of angle from one.
2. The quotient of subtraction of tan cubed of angle from three times tan of angle by subtraction of three times tan squared of angle from one is simplified as tan of triple angle.

#### How to use

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,

$(1) \,\,\,\,\,\,$ $\tan{3x} \,=\, \dfrac{3\tan{x}-\tan^3{x}}{1-3\tan^2{x}}$

$(2) \,\,\,\,\,\,$ $\tan{3A} \,=\, \dfrac{3\tan{A}-\tan^3{A}}{1-3\tan^2{A}}$

$(3) \,\,\,\,\,\,$ $\tan{3\alpha} \,=\, \dfrac{3\tan{\alpha}-\tan^3{\alpha}}{1-3\tan^2{\alpha}}$

#### Proof

Learn how to derive the rule of tan triple angle identity by geometry in trigonometry.

###### Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Practice now

###### Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

###### Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.