# Cot Double angle formula

### Expansion form

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

### Simplified form

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

### Introduction

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

1. Cot of double angle is expanded as the quotient of subtraction of one from square of cot function by twice the cot function.
2. The quotient of subtraction of one from square of cot function by twice the cot function is simplified as cot of double angle.

#### How to use

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

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

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

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

#### Proof

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

Latest Math Topics
Apr 18, 2022
Apr 14, 2022
Mar 18, 2022
Latest Math Problems
Apr 06, 2022

A best free mathematics education website for students, teachers and researchers.

###### Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

###### Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

###### Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.