arccot(x) + arccot(y) = arccot( $\frac{xy - 1}{y + x}$ )

We will learn how to prove the property of the inverse trigonometric function arccot(x) + arccot(y) = arccot( $\frac{xy - 1}{y + x}$ ) (i.e., cot $^{-1}$ x - cot $^{-1}$ y = cot $^{-1}$ ( $\frac{xy - 1}{y + x}$ )

Proof:

Let, cot $^{-1}$ x = α and cot $^{-1}$ y = β

From cot $^{-1}$ x = α we get,

x = cot α

and from cot $^{-1}$ y = β we get,

y = cot β

Now, cot (α + β) = ( $\frac{cot α cot β - 1}{cot β + tan α}$ )

cot (α + β) = $\frac{xy - 1}{y + x}$

⇒ α + β = cot $^{-1}$ $\frac{xy - 1}{y + x}$

⇒ cot $^{-1}$ x + cot $^{-1}$ y = cot $^{-1}$ $\frac{xy - 1}{y + x}$

Therefore, cot $^{-1}$ x + cot $^{-1}$ y = cot $^{-1}$ $\frac{xy - 1}{y + x}$

● Inverse Trigonometric Functions

11 and 12 Grade Math

From arccot(x) + arccot(y) to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Facebook X Pinterest WhatsApp Messenger

[?]Subscribe To This Site

$XML RSS$

Recent Articles

Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume
Jul 20, 25 12:58 PM
$Volume of Cuboid$
Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…
Read More
5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units
Jul 20, 25 10:22 AM
$Cubes in Cuboid$
Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…
Read More
Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan
Jul 19, 25 05:00 AM
$Area and Perimeter of Square and Rectangle$
We will practice the questions given in the worksheet on area of a square and rectangle. We know the amount of surface that a plane figure covers is called its area. 1. Find the area of the square len…
Read More
Area of Rectangle Square and Triangle | Formulas| Area of Plane Shapes
Jul 18, 25 10:38 AM
$Area of a Square of Side 1 cm$
Area of a closed plane figure is the amount of surface enclosed within its boundary. Look at the given figures. The shaded region of each figure denotes its area. The standard unit, generally used for…
Read More
What is Area in Maths? | Units to find Area | Conversion Table of Area
Jul 17, 25 01:06 AM
$Concept of Area$
The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…
Read More

E-mail Address

First Name

Then Don't worry — your e-mail address is totally secure. I promise to use it only to send you Math Only Math.

arccot(x) + arccot(y) = arccot(xy−1y+x\frac{xy - 1}{y + x})

New! Comments

Recent Articles

Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan

Area of Rectangle Square and Triangle | Formulas| Area of Plane Shapes

What is Area in Maths? | Units to find Area | Conversion Table of Area

arccot(x) + arccot(y) = arccot( $\frac{xy - 1}{y + x}$ )