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

A trigonometric identity that expresses the expansion of sine of double angle function in terms of tan function is called the sine of double angle identity in tangent function.

When the symbol theta represents an angle of a right triangle, the sine and tangent functions are written as $\sin{\theta}$ and $\tan{\theta}$ respectively. In the same way, the sine of double angle function is written as $\sin{(2\theta)}$ mathematically.

The sine double angle function can be expressed in terms of tan functions in the following rational form.

$\implies$ $\sin{2\theta}$ $\,=\,$ $\dfrac{2\tan{\theta}}{1+\tan^2{\theta}}$

The sine of double angle formula in terms of tan function is used in two cases in trigonometric mathematics.

It is used to expand the sine of double angle function in terms of tan of angle function.

$\implies$ $\sin{2\theta}$ $\,=\,$ $\dfrac{2\tan{\theta}}{1+\tan^2{\theta}}$

It is also used to simplify the following form rational expression as the sine of double angle function.

$\implies$ $\dfrac{2\tan{\theta}}{1+\tan^2{\theta}}$ $\,=\,$ $\sin{2\theta}$

The angle in the sin double angle formula can be denoted by any symbol. Therefore, the following three are popular forms of sine of double angle identity in terms of tangent.

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

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

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

Learn how to prove the sine of double angle identity in terms of tan of angle in trigonometry mathematics.

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 2022

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 - 2021 Math Doubts, All Rights Reserved