# 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

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.

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

## Recent Articles

1. ### Addition and Subtraction of Fractions | Solved Examples | Worksheet

Jul 18, 24 03:08 PM

Addition and subtraction of fractions are discussed here with examples. To add or subtract two or more fractions, proceed as under: (i) Convert the mixed fractions (if any.) or natural numbers

2. ### Worksheet on Simplification | Simplify Expressions | BODMAS Questions

Jul 18, 24 01:19 AM

In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet

3. ### Fractions in Descending Order |Arranging Fractions an Descending Order

Jul 18, 24 01:15 AM

We will discuss here how to arrange the fractions in descending order. Solved examples for arranging in descending order: 1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order. First…

4. ### Fractions in Ascending Order | Arranging Fractions | Worksheet |Answer

Jul 18, 24 01:02 AM

We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we fi…