$\tan{(A+B)}$ $\,=\,$ $\dfrac{\tan{A}+\tan{B}}{1\,–\,\tan{A}\tan{B}}$

$\dfrac{\tan{A}+\tan{B}}{1\,–\,\tan{A}\tan{B}}$ $\,=\,$ $\tan{(A+B)}$

The tan of angle sum identity is called as tan of sum of two angles identity or tan of compound angle identity. It is mainly used in mathematics in two cases possibly.

- To expand tan of sum of two angles as the quotient of sum of tangents of angles by the subtraction of products of tangents of both angles from one.
- To simplify the quotient of sum of tangents of angles by the subtraction of products of tangents of both angles from one as tan of sum of two angles.

The tan of angle sum identity is written in several ways in which $\tan{(A+B)}$, $\tan{(x+y)}$ and $\tan{(\alpha+\beta)}$ are popular in the world. You can write it in terms of any two angles.

$(1) \,\,\,\,\,\,$ $\tan{(A+B)}$ $\,=\,$ $\dfrac{\tan{A}+\tan{B}}{1\,–\,\tan{A}\tan{B}}$

$(2) \,\,\,\,\,\,$ $\tan{(x+y)}$ $\,=\,$ $\dfrac{\tan{x}+\tan{y}}{1\,–\,\tan{x}\tan{y}}$

$(3) \,\,\,\,\,\,$ $\tan{(\alpha+\beta)}$ $\,=\,$ $\dfrac{\tan{\alpha}+\tan{\beta}}{1\,–\,\tan{\alpha}\tan{\beta}}$

You have learned the tan of sum of two angles formula and let’s learn how the tan of angle sum identity is derived in mathematical form by the geometrical approach.

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.