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

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

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

- 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.
- 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.

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.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.