$(1).\,\,$ $\cot{(a+b)}$ $\,=\,$ $\dfrac{\cot{b}\cot{a}-1}{\cot{b}+\cot{a}}$

$(2).\,\,$ $\cot{(x+y)}$ $\,=\,$ $\dfrac{\cot{y}\cot{x}-1}{\cot{y}+\cot{x}}$

Let’s assume that $a$ and $b$ are two variables, which are used to represent two angles. In mathematics, the sum of two angles is written as $a+b$, which is actually a compound angle. The cotangent of a compound angle $a$ plus $b$ is written as $\cot{(a+b)}$ in trigonometric mathematics.

The cotangent of the sum of angles $a$ and $b$ is equal to the quotient of the subtraction of one from the product of cotangents of angles $a$ and $b$ by the sum of the cotangents of angles $a$ and $b$.

$\cot{(a+b)}$ $\,=\,$ $\dfrac{\cot{b} \times \cot{a}-1}{\cot{b}+\cot{a}}$

This mathematical equation is called the cotangent of angle sum trigonometric identity in mathematics.

The cot angle sum identity is possibly used in two cases in trigonometric mathematics.

The cot of the sum of two angles is expanded as the quotient of the subtraction of one from the product of cotangents of angles by the sum of the cotangents of angles.

$\implies$ $\cot{(a+b)}$ $\,=\,$ $\dfrac{\cot{(b)}\cot{(a)}-1}{\cot{(b)}+\cot{(a)}}$

The quotient of the subtraction of one from the product of cotangents of angles by the sum of the cotangents of angles is simplified as the cot of the sum of two angles.

$\implies$ $\dfrac{\cot{(b)}\cot{(a)}-1}{\cot{(b)}+\cot{(a)}}$ $\,=\,$ $\cot{(a+b)}$

The angle sum trigonometric formula in cotangent function is written in several forms but it is popularly expressed in the following three forms.

$(1).\,\,$ $\cot{(A+B)}$ $\,=\,$ $\dfrac{\cot{B}\cot{A}-1}{\cot{B}+\cot{A}}$

$(2).\,\,$ $\cot{(x+y)}$ $\,=\,$ $\dfrac{\cot{y}\cot{x}-1}{\cot{y}+\cot{x}}$

$(3).\,\,$ $\cot{(\alpha+\beta)}$ $\,=\,$ $\dfrac{\cot{\beta}\cot{\alpha}-1}{\cot{\beta}+\cot{\alpha}}$

Learn how to derive the cot of angle sum trigonometric identity by a geometric method in trigonometry.

Latest Math Topics

Jan 06, 2023

Jan 03, 2023

Jan 01, 2023

Dec 26, 2022

Dec 08, 2022

Latest Math Problems

Jan 31, 2023

Nov 25, 2022

Nov 02, 2022

Oct 26, 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 - 2022 Math Doubts, All Rights Reserved