# Important Properties of Inverse Trigonometric Functions

Inverse trigonometric functions are an essential part of mathematics examinations. That is, every class 12 student needs to be well-equipped with this chapter. This chapter deals with various trigonometric formulas that are highly useful for you.

That is why you can refer to this guide, where we have listed down the essential properties of Inverse Trigonometric Functions Class 12. So, make sure you stick with us until the end for more.

## Properties of Inverse Trigonometric Functions

Before you start, make sure you know some basic Inverse Trigonometric Functions to learn about. These are important to solve diverse problems and help understand the idea of Inverse Trigonometric Functions in a more comprehensive order.

Read: Uses and Importance of Mathematics in Day to Day Life

So, let us look at the different properties.

Property 1

Sin-1 (1/x) = cosec -1 x, x ≥1 or x ≤ -1

1. Cos-1 (1/x) = sec -1 x, x ≥1 or x ≤ -1
2. Tan-1 (1/x) = cot -1 x, x > 0

Property 2

1. Sin-1 (-y) = – sin-1 (y), y ϵ (-1, 1)
2. Tan-1 (-y) = – tan-1 (y), y ϵ R
3. Cosec -1 (-y) = – cosec -1 (y), | y | ≥1

Property 3

1. Cos-1 (-x) = π- cos -1 x, x ϵ (-1, 1)
2. Sec-1 (-x) = π-sec -1 x | x | ≥1
3. Cot-1 (-x) = π -cot -1 x, x ϵ R

Property 4

1. Sin-1a + Cos-1 x = π/2, x ϵ (-1, 1)
2. Tan-1 x + Cot-1 x = π/2, x ϵ R
3. Cosec-1 x+ Sec -1 x = π/2, | x | ≥1

Property 5

1. Tan-1 x -Tan-1y= Tan-1 ((x+ y) / (1-xy)), xy <1
2. Tan-1 x – Tan-1 y = Tan-1((x+ y) / (1+xy)), xy > -1

Property 6

1. 2tan-1 x = tan-1 (2x (1 +x2)), | x | ≤ 1
2. 2tan-1 x = cos-1 (2x (1- x2)/ (1+ x2)), x ≥ 0
3. 2tan-1 x = tan-1(2x (1- x2)), -1 < x < 1

## How to Improve in Inverse Trigonometric Functions?

1. ### Practice Thoroughly

One of the best ways to improve in Inverse Trigonometric Functions Class 12 is to practice consistently. Practice can help you to improve in this subject each day. It will allow you to make mistakes and learn from them all over again.

Practicing consistently may also sharpen your mathematical skills and help you score good grades on time. That is why we recommend you to indulge in it without any failure.

1. ### Get a Good Book

If you cannot solve Inverse Trigonometric Functions Class 12 correctly, maybe you need a good book. Yes, a comprehensive guide on this chapter with a more straightforward explanation might be able to help you understand it faster.

As a result, you may not have to keep brainstorming and wondering how to improve in it.

1. ### List Down the Formulas Together

Generally, the essential formulas for Inverse Trigonometric Functions Class 12 are all scattered in the book. This could drain you enough time only in looking for them and remembering them correctly.

However, if you have them listed in a single paper, it will be easier to remember them. So, why keep waiting? Make sure you create a list of all the essential formulas of inverse trigonometric functions for best practice.

### The Bottom Line

We all know that it is crucial to be well-versed with Inverse Trigonometric Functions Class 12. So, why keep wasting time? Make sure you start today for the best experience.