##### Aakash iACST Scholarship Test 2024

ApplyGet up to 90% scholarship on NEET, JEE & Foundation courses

Edited By Kuldeep Maurya | Updated on Jan 21, 2022 11:34 AM IST

RD Sharma class 12th exercise 3.11 is an excellent NCERT solutions book that comes highly recommended by students from all over the country. RD Sharma solutions have been popular among high school students and teachers for a long time now. Their solutions are praised for being simple and easy to understand. The RD Sharma class 12 solutions chapter 3 ex 3.11, like any other RD Sharma book, has been specially formulated by experts from the education sector who have a lot of knowledge on the subject. RD Sharma solutions Their expertise in solving mathematical problems is evident as the solutions contain simple tips and tricks to help you solve the questions faster. So, you can follow their methods and guidelines to understand the concepts better and score well in exams.

RD Sharma Class 12 Solutions Chapter 3 Inverse Trigonometric Functions - Other Exercise

- Chapter 3 - Inverse Trigonometric Ex 3.1
- Chapter 3 - Inverse Trigonometric Ex 3.2
- Chapter 3 - Inverse Trigonometric Ex 3.3
- Chapter 3 - Inverse Trigonometric Ex 3.4
- Chapter 3 - Inverse Trigonometric Ex 3.5
- Chapter 3 - Inverse Trigonometric Ex 3.6
- Chapter 3 - Inverse Trigonometric Ex 3.7
- Chapter 3 - Inverse Trigonometric Ex 3.8
- Chapter 3 - Inverse Trigonometric Ex 3.9
- Chapter 3 - Inverse Trigonometric Ex 3.10
- Chapter 3 - Inverse Trigonometric Ex 3.12
- Chapter 3 - Inverse Trigonometric Ex 3.14
- Chapter 3 - Inverse Trigonometric Ex VSA

Inverse Trigonometric Function Exercise 3.11 Question 1(i)

There is one formula in trigonometric function for union.

Let’s see the formula,

In LHS side,

Let

Let’s take LHS

L.H.S

Let’s use formula,

Let’s put the value of x and y in formula

Hence, the prove

Inverse Trigonometric Function Exercise 3.11 Question 1(ii).

To solve this type of question, we must convert and in using hypotenuse theorem.

For proving this type of question,

Let’s assume,

So, we have to prove that

First of all

Using the formula of hypotenuse , third side will be 5.

Also we have,

Using the formula of hypotenuse, third side will be 3

…(ii)

Also we have,

Let’s take tan on both sides,

Let’s put value, from (i), (ii) and (iii)

∴ L.H.S =R.H.S

Hence, the prove

Inverse Trigonometric Function Exercise 3.11 Question 1(iii).

For solving this, we can use the formula of union trigonometric function,

L.H.S

Let’s take

So, [Removing inverse]

Using the formula of hypotenuse , Hypotenuse =

Let’s put value of (ii) into (i)

… (iii)

So, =R.H.S

Hence, the prove

Note: We must remember the formula of hypotenuse.

Inverse Trigonometric Function Exercise 3.11 Question 2.

For solving this, we can use the formula of union trigonometric function,

Let’s use the formula

Where

Inverse Trigonometric Function Exercise 3.11 Question 3(i).

For solving this, we can use the formula of union trigonometric function,

and we have to find the value of x.

Here A=2x and B=3x

So, let’s put the values of A and B in the formula of

Inverse Trigonometric Function Exercise 3.11 Question 3(ii).

Here, we can use the below formula,

Here, A=x+1

B=x-1

So, let’s put the values of A and B in the formula of

Inverse Trigonometric Function Exercise 3.11 Question 3(iii).

Here, we can use the formula of union trigonometric function,

We have to solve and find the value of x.

L.H.S=R.H.S

Let’s use in sum formula,

Inverse Trigonometric Function Exercise 3.11 Question 3(iv).

Answer:Hint:

Here, we use the formula of Intersection

Given:

Solution:

Here let’s assume

Inverse Trigonometric Function Exercise 3.11 Question 3(v).

Here, we use the formula of Intersection

We know that,

Therefore, the given equation converted into

Inverse Trigonometric Function Exercise 3.11 Question 3(vi)

Answer:Hint:

Here, we use the formula

Given:

Solution:

Here we have

Using the value of A and B in the formula of

Hint:

Here, we use the below formula

Given:

for

Solution:

Using the values of A and B in the formula of , we get

Inverse Trigonometric Function Exercise 3.11 Question 3(viii).:

Here, we will use the formula

Inverse Trigonometric Function Exercise 3.11 Question 3(ix).

Here, we will use the formula

Inverse Trigonometric Function Exercise 3.11 Question 3(x)

Here, we will use the formula

Inverse Trigonometric Function Exercise 3.11 Question 3(xi).

Here, we use the below formula

Here A=4x

B=6x

Let’s put the values of A and B in formula of ,we get

We have to focus on calculation of infinite series.

The RD Sharma class 12 chapter 3 exercise 3.11 book is based on the chapter Inverse Trigonometric Function. This chapter was also introduced in class 11, where students had learned the basic concepts of trigonometry. Exercise 3.11 in this chapter has a total of 16 questions, which are divided into levels 1 and 2. They are mostly addition and equation questions in trigonometry. The chapter on Inverse Trigonometric Functions is a critical chapter that needs special attention from students.

Self-practice at home will immensely help improve students' clarity on concepts and help them solve questions faster. For this reason, class 12 RD Sharma chapter 3 exercise 3.11 solution will be beneficial for students to check their performance and mark their answers. By doing this, they will pinpoint their doubts and weak points to work on them. Moreover, the RD Sharma class 12th exercise 3.11 is constantly updated according to the latest syllabus, so you can be sure to find all answers you require.

The RD Sharma class 12 solutions Inverse Trigonometric Function ex 3.11 can be an excellent guide to students who like to practice solving questions at home. Students who have practiced with RD Sharma solutions have confirmed that they have found common questions in board exams. Therefore, using RD Sharma class 12 chapter 3 exercise 3.11 can help better your chances at finding common questions in the board paper.

Teachers too like to use RD Sharma class 12th exercise 3.11 to give homework questions to students in class 12. You can seek the help of these solutions to check your progress through the chapters and know if you have understood everything. The best thing about these books is that they are easily available online at Career360 and come completely free of cost. You can download the pdf online and use it anytime you want.

**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. What are the benefits of using RD Sharma class 12th exercise 3.11 solutions?

RD Sharma solutions have helped thousands of students to score well in board exams, especially in their mathematics papers. Their answers are crafted by experts from the country who know how to solve complex math problems simply. Sometimes questions from the book appear on board papers, which helps students to score better. The book is continually updated with the latest syllabus so that you will find all answers here.

2. Will I get common questions in the board exam if I study RD Sharma solutions?

Many students who have appeared for board exams expressed their love for RD Sharma solutions due to the quality of answers in the book. They have also confirmed that the questions in RD Sharma solutions have appeared in board exams, and they were able to solve them pretty easily. So, if you use RD Sharma solutions, you can find common questions in your board paper.

3. Is the RD Sharma solution book good for solving homework?

The RD Sharma class 12th exercise 3.11 is used by school teachers to give homework to students and prepare school test papers. Therefore, the solutions provided in the book can be used by students to solve their homework questions and complete their home tasks faster.

4. Where can I find the RD Sharma class 12 solutions chapter 3 ex 3.11 book?

There is no need to go to stores and purchase expensive books for study material. Instead, you can simply download the soft copy or pdf of RD Sharma class 12 solutions chapter 3 ex 3.11, available on Career360. This is your one-stop solution for RD Sharma books, which come completely free of cost.

5. Is it necessary to practice Trigonometric questions at home?

Chapter 3 of the mathematical book is on Inverse Trigonometric function, which is quite difficult to ace if you do not practice at home. Therefore, it is always recommended you use RD Sharma class 12th exercise 3.11 to practice at home and test your knowledge by comparing the answer in the book. This will help you understand the concepts better and enhance your problem-solving skills.

May 20, 2024

May 20, 2024

Get answers from students and experts

Get up to 90% scholarship on NEET, JEE & Foundation courses

Register FREE for ALLEN Digital Scholarship Admission Test (ADSAT)

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

Enrol in PW Vidyapeeth center for JEE coaching

Enrol in PW Vidyapeeth center for NEET coaching

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

News and Notifications

19/05/2024, 15:50:17

19/05/2024, 12:36:34

19/05/2024, 07:06:39

18/05/2024, 10:25:51

17/05/2024, 08:35:26

13/05/2024, 12:38:42

10/05/2024, 13:31:17

Back to top