##### VMC VIQ Scholarship Test

ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Edited By Kuldeep Maurya | Updated on Jan 21, 2022 11:59 AM IST

RD Sharma solutions are pretty popular and well-known among students and teachers. They have been involved in making NCERT solutions for a very long time and have already established their books to be the perfect guide for home study. The RD Sharma class 12th exercise 3.3 is one such NCERT solution set that is extremely helpful to students who have opted for the mathematics subject. RD Sharma class 12 chapter 3 exercise 3.3 is a great book section on NCERT solution that focuses on the third chapter of the mathematics book. Chapter 3 of the book deals with Inverse Trigonometric Functions, which is a critical chapter with many complicated theories. The solutions have nine questions, including subparts in level 1, which cover the concept of principal values.

**JEE Main 2025: Sample Papers | Mock Tests | PYQs | Study Plan 100 Days**

**JEE Main 2025: Maths Formulas | Study Materials**

**JEE Main 2025: Syllabus | Preparation Guide | High Scoring Topics **

- Chapter 3 - Inverse Trigonometric Functions Ex 3.1
- Chapter 3 - Inverse Trigonometric Functions Ex 3.2
- Chapter 3 - Inverse Trigonometric Functions Ex 3.4
- Chapter 3 - Inverse Trigonometric Functions Ex 3.5
- Chapter 3 - Inverse Trigonometric Functions Ex 3.6
- Chapter 3 - Inverse Trigonometric Functions Ex 3.7
- Chapter 3 - Inverse Trigonometric Functions Ex 3.8
- Chapter 3 - Inverse Trigonometric Functions Ex 3.9
- Chapter 3 - Inverse Trigonometric Functions Ex 3.10
- Chapter 3 - Inverse Trigonometric Functions Ex 3.11
- Chapter 3 - Inverse Trigonometric Functions Ex 3.12
- Chapter 3 - Inverse Trigonometric Ex 3.13
- Chapter 3 - Inverse Trigonometric Functions Ex 3.14
- Chapter 3 - Inverse Trigonometric Ex VSA

Inverse Trigonometric Functions Exercise 3.3 Question 1 (i)

Let .....(i)

[ From equation (i) ]

The range of principal value branch of is

Hence, principal value of .

Inverse Trigonometric Functions Exercise 3.3 Question 1 (ii)

Let ....(i)

[From equation (i)]

The range of principal value branch of is

Hence, principal value of .

Inverse Trigonometric Functions Exercise 3.3 Question 1 (iii)

**Answer :** 0**Hint :** The branch with range is called the principal value branch of function .**Given :****Explanation :**

Let ....(i)

The range of principal value branch of is .

Hence, the principal value of is 0.

Thus,

Let ....(i)

The range of principal value branch of is .

Hence, the principal value of is .

Inverse Trigonometric Functions Exercise 3.3 Question 2 (i)

Thus,

The branch with range is called the principal value branch of the function and domain of the function.

Thus,

Let us first solve for

Let ....(i)

[from equation (i)]

The range of principal value branch of is .

.....(ii)

Let us solve for

Let .....(iii)

[From equation (iii)]

The range of principal value branch of is .

.....(iv)

Now,

[From equation (ii) and (iv)]

.

Inverse Trigonometric Functions Exercise 3.3 Question 2 (ii)

Thus,

The branch with range is called the principal value branch of the function and domain of the function is .

Thus,

Let is first solve for .

Let, .....(i)

The range of principal value branch of is .

The principal value of is .....(ii)

Now,

[From equation (ii)]

.....(iii)

Now,

Let ......(iv)

[From equation iv]

The range of principal value branch of is .

Principal value of is .

Hence principal vaue of is .

Inverse Trignometric Function Exercise 3.3 Question 3 (i) .

Answer :Hint : The branch with range is called the principal value branch of function .

Thus,

The branch with range is called the principal value branch of the function .

Thus,

The branch with range is called the principal value branch.

Thus,

Domain of functions and are and respectively.

Given :

Explanation :

Let us first solve for

Let

...(i)

[From equation (i)]

Range of principal value branch of is

Therefore principal of value of is ....(ii)

Now,

Let us solve for

Let ....(iii)

[From equation (iii)]

The range of principal value branch of is .

Principal value of ......(iv)

Now,

Let us solve for

Let ....(v)

[From equation (v)]

The range of principal value branch of is .

Principal value of is ...(vi)

Now,

Putting the values from equations (ii), (iv) and (vi)

Inverse Trignometric Function Exercise 3.3 Question 3 (ii) .

Answer :Hint : The branch with range is called the principal value branch of function .

Given :

Explanation :

Let us first solve for

Let

[From equation (i) ]

The range of principal value branch of is .

Hence principal value of ... (ii)

Now,

Let us solve for

Let ...(iii)

[From equation (iii)]

The Range of principal value branch of is .

Hence principal value of ...(iv)

Now,

Let us solve for

The Range of principal value branch of is .

Hence principal value .....(v)

Now consider

From equation (ii), (iv) and (v)

Inverse Trignometric Function Exercise 3.3 Question 3 (iii) .

**Answer :** 0**Given : ****Explanation :**

The RD Sharma class 12 solutions chapter 3 ex 3.3 seeks to provide answers and solutions to all the questions present in the NCERT books. The class 10 RD Sharma chapter 3 exercise 3.3 solution has only expert-created solutions for students. The experts who have written and compiled the answer are highly skilled and have a lot of knowledge in mathematics. Moreover, they have provided some new and improved ways of solving mathematical problems, which would make it easier for you to answer the questions. These unique methods you will find only in class 12 RD Sharma chapter 3 exercise 3.3 solution.

The answers provided in RD Sharma class 12 solutions Inverse Trigonometry Function ex 3.3 are simple to follow and easily understood by students. The detailed answers and steps will be of immense help to students to improve their knowledge of Inverse Trigonometry. Using these solutions will be able to clear their doubts and focus on their weak points to make improvements. With the help of the RD Sharma class 12th exercise 3.3, you will learn everything in detail and score high in your exams.

Since RD Sharma is a trusted source for solutions, teachers like to use these books to give homework to students. Students having difficulty completing homework on their own can use these books to get some help. They will find all the answers to the questions that are in the NCERT book. The pdf of RD Sharma class 12 solutions chapter 3 ex 3.3 is updated every year to include the latest syllabus so that you are not left wanting in any way.

RD Sharma class 12th exercise 3.3 Solutions is the top choice for students for board exam preparations and self-practice at home. You can easily trust them to help you improve and enhance your knowledge so that you won't have to purchase too many study materials. You will find the pdf of class 12 RD Sharma chapter 3 exercise 3.3 solution online on Career360, which is the one-stop destination for RD Sharma solutions. These pdfs are available to download at any time and are completely free of cost. With all these benefits of using RD Sharma solutions, you can be sure that the book will help you.

**Chapter-wise RD Sharma Class 12 Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. How can I avail myself the class 12 RD Sharma chapter 3 exercise 3.3 solution?

Finding the downloading the class 12 RD Sharma chapter 3 exercise 3.3 solution is very easy. All you have to do is navigate to the Career360 website and download the free pdf of the book from there. The pdf of the book is always available and does not require any subscription fees at all.

2. What are the benefits of using RD Sharma class 12th exercise 3.3 solutions?

Students and teachers have trusted the RD Sharma class 12th exercise 3.3 solutions for a long time. They have already asserted that students who have practiced the NCERT solutions have found common questions in the board exams. The solutions will also help you to test your knowledge at home and improve upon your weak areas.

3. Are our RD Sharma solutions updated according to the latest syllabus?

RD Sharma seeks to include all the answers to the questions in the NCERT book. For this reason, they are updated every year to include the latest syllabus of CBSE class 12. Therefore, you can be entirely sure that the book will have all the answers you require. All you have to do is download the correct file according to your exam year.

4. Which is the best NCERT solution for solving homework?

There are many NCERT solutions online, which offer homework solutions to students. However, RD Sharma solutions are easily the most trusted book that is followed by thousands of students. Teachers also like to use these books to provide home tasks, so they are very useful when solving homework problem

5. Are RD Sharma solutions expensive?

RD Sharma Solutions are not all expensive. They are entirely free of cost and don't come with any hidden fees. You can download the soft copy of the book from Career360, which has the latest and updated versions of the books. In addition, you can print out the pdf, which can be done for a nominal amount.

Get answers from students and experts

Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer! Trusted by 3,500+ universities globally

News and Notifications

Back to top