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

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

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

- Tan of double angle is expanded as the quotient of twice the tan function by subtraction of square of tan function from one.
- The quotient of twice the tan function by subtraction of square of tan function from one is simplified as tan of double angle.

The tangent of double angle identity is used to either expand or simplify the double angle functions like $\tan{2A}$, $\tan{2x}$, $\tan{2\alpha}$ and etc. For example,

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

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

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

Learn how to derive the rule of tan double angle identity by geometric approach in trigonometry.

Latest Math Topics

Mar 21, 2023

Feb 25, 2023

Feb 17, 2023

Feb 10, 2023

Jan 15, 2023

Latest Math Problems

Mar 03, 2023

Mar 01, 2023

Feb 27, 2023

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 math problems in different methods with understandable steps and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved