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

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

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

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved