# RS Aggarwal Class 12 Chapter 4 Solutions (Inverse Trigonometric Functions)

RS Aggarwal Solutions for Class 12 Chapter 4 is prepared to help you build a strong understanding of Inverse Trigonometric Functions. There are 5 exercises and 126 questions in this chapter. In this chapter, we will learn about the properties of the inverse trigonometric functions. The exercise-wise solutions discuss in detail the method of finding principal values of the given inverse functions. The solutions are prepared by the subject matter experts of Instasolv, which is 100% accurate and error-free.

In Chapter 4 of RS Aggarwal Solutions, we will also learn to represent these functions on graphs after studying the range and domain of each inverse trigonometric function thoroughly. It is a recurring topic in most important All India Entrance Exams and Class 12 Board exam, and hence the RS Aggarwal Solutions for Class 12 Chapter 4 is a very important resource for preparing this chapter.

The solutions prepared by Instasolv are aligned with the frequently occurring queries of students of Class 12. The team of subject matter experts at Instasolv have prepared the solutions to give you a quality source of reference. All the questions are solved in the solutions for RS Aggarwal Class 12 Chapter 4. You will find the answers in a step by step format for all the concepts and properties of the inverse trigonometric function.

## Important Points of RS Aggarwal Solutions for Class 12 Chapter 4 Inverse Trigonometric Functions

**Introduction to Inverse of a Function:**

In this chapter, we shall use the concepts of functions studied in the previous chapters to find the inverses of the trigonometric functions. We will begin with first recalling the definition of the inverse of a function.

Corresponding to every bijection f: A → B, there exists a bijection g: B → A defined by :

g(y) = x if and only if f(x) = y

Here, g(y) is the inverse of f(x) and is denoted by f^{-1}.

**Basic Concepts:**

The following table gives the domains, ranges and the principal values of all trigonometric functions:

Note: If there is no mention about the branch of the inverse trigonometric function, you must assume it to be the principal value branch of that function.

### Properties of Inverse Trigonometric Functions

**Highlights:**

- It should be noted that all trigonometric functions do not have inverse functions but if their domains and codomains are restricted they can be made one-one onto function and their inverse functions can be found easily.
- We draw the graphs of inverse trigonometric functions using the graphs of corresponding trigonometric functions by interchanging the coordinate axes or by taking their image in the line mirror.

### Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 4 Inverse Trigonometric Functions

- You will learn how to find the principal values of the inverse trigonometric functions given in the questions in the initial exercises. You will also have to prove some equations related to these functions in the solutions of the third and fourth exercises.
- In the exercise questions, you will learn various new properties and their proofs with the help of the basic properties studied in this chapter.
- You will be required to draw the graphs of different inverse trigonometric functions in the 4th exercise.
- The exercise questions consist of beginners as well as advanced level questions for the RS Aggarwal Class 12 Maths Solutions board exams as well as important national level competitive entrance exams.
- The solutions are prepared in such a manner that all the important topics are covered and solutions are given in an easy-to-understand language.

## Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 4 by Instasolv

### The subject matter experts of mathematics at Instasolv have curated step by step solutions for all the questions of every exercise of Chapter 4- Inverse Trigonometric Functions.

- The format of the solutions is in accordance with the board guidelines.
- You will learn to manage time optimally once you will have practised the solutions by Instasolv.