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RD Sharma Solutions

RD Sharma Class 12 Maths Solutions Chapter 4 - Inverse Trigonometric Functions

RD Sharma Class 12 Maths Solutions Chapter 4 - Inverse Trigonometric Functions

Q: 8. What is a common mistake when simplifying expressions like cos(cos⁻¹x), and how do the solutions address this?

A common mistake is to assume cos(cos⁻¹x) is always 'x' without checking its value. This property only holds if 'x' is within the domain of cos⁻¹x, which is [-1, 1]. The RD Sharma solutions meticulously point this out, teaching students to first verify the domain and range constraints before applying any simplification formula, a critical habit for scoring full marks.

Q: 9. Can mastering Chapter 4 from RD Sharma solutions help in other advanced topics like Calculus?

Absolutely. A strong understanding of the properties and graphs of inverse trigonometric functions is a prerequisite for Calculus. The detailed methods in these solutions build a solid foundation that is directly applicable when you need to find the derivatives and integrals of inverse functions in later chapters, making those complex calculus problems much easier to solve.

RD Sharma Solutions for Class 12 Maths - Inverse Trigonometric Functions - Free PDF Download

Inverse Trigonometric Functions Class 12 RD Sharma gives detailed solutions to all types of questions which are asked in exams. The free PDF of Class 12 RD Sharma Solutions Chapter 4 are prepared by the experts on the latest CBSE syllabus. The solutions are carefully prepared to provide a step-by-step approach so that students will get their doubts cleared when referring through the PDF. The free PDF also contains an excess amount of questions and solutions along with practice problems for students to improve their knowledge of Inverse trigonometry.

Class 12 RD Sharma Textbook Solutions Chapter 4 - Inverse Trigonometric Functions

RD Sharma Class 12 Maths Solutions Inverse Trigonometry

Inverse trigonometry is one of the important chapters for Class 12 students because in this chapter we find inverses of 6 fundamental trigonometric functions, along with that we use these inverse trigonometric properties to obtain an angle from any of the trigonometric ratios. In engineering, navigation, physics, and geometry, inverse trigonometric functions are commonly used.

We have provided step by step solutions for all exercise questions given in the pdf of Class 12 RD Sharma Chapter 4 - Inverse Trigonometric Functions. Have a look at Exercise 4.1

Some of the Important Concepts of Inverse Trigonometry Discussed in This Chapter Are as Follows

Introduction and recall the basic concepts of trigonometry
Finding the inverse of the sine function, cosine function, tangent function, cotangent function, secant function, and cosecant function.
Properties of inverse trigonometric functions which gives the relationship between different inverse trigonometric functions.

Tips on How to Prepare for Exams Using Inverse Trigonometric Functions Class 12 RD Sharma

Vedantu provides top-notch content on inverse trigonometry questions as per CBSE exam pattern and weightage of the marks. Students can follow these tips when going through RD Sharma Class 12 Inverse Trigonometry Solutions.

First, brush up on the basics of trigonometric functions before finding the inverse of those.
Read the question carefully before answering. When solving RD Sharma questions students are advised not to look at the solutions directly. First, solve the solutions on your own and later compare with RD Sharma Class 12 Maths Solutions Inverse Trigonometry. Later students can compare their solutions with the RD Sharma PDF notes.
Since Vedantu provides a step-by-step approach to solutions, students can easily prepare without missing any steps. This also makes students have a grasp of all intermediate steps used while solving the problems.
For more subject knowledge on the topic, students can solve the extra practice and exercise problems to ace their exams.

For the preparation of your Maths board exams, your greatest study partner will be RD Sharma Class 12 Maths Solutions Chapter 4: Inverse Trigonometric Functions. You'll learn about the inverse of the sine function, cosine, as well as other trigonometric functions like tan, cot, and cosec in this chapter of RD Sharma Solutions. In addition, the properties of the inverse of trigonometric functions are discussed in this chapter.

This chapter contains 14 exercises and almost 300 questions to practise. Hence, RD Sharma Class 12 Maths book is an excellent instrument for completely practising math concepts because it has a wide range of questions. There are also past year questions from the CBSE board exam for class 12 in this chapter. As a result, you must practise all of the questions in order to prepare for the board exams.

In Class 12 Maths Chapter 4, you will study that if a= f(a) and b= g(b) are two functions so that f (g(a)) = b and g (f(b)) = a, then f and g are seen to be inverse of each other, i.e. g = f^-1.

When a function is bijective, there exists an inverse of it. When the domain of trigonometric functions is constrained, the functions become bijective, and the inverse of trigonometric functions is always defined inside the constrained domain. The symbol 'f-1' is used to represent the inverse of a function.

The inverses of many trigonometric functions, such as sine^-1, cos^-1, tan^-1, cosec^-1, sec^-1, and cot^-1, will be discussed later in the chapter. You'll also learn about these functions' domain and range, as well as several key properties that can assist you in solving inverse trigonometric function problems.

Inverse functions can be used to calculate the angle from any trigonometric ratio. All of these ratios have applications in a variety of fields, including engineering, geometry, and physics.

According to the CBSE exam structure, Vedantu provides high-level content on inverse trigonometry questions. We primarily focus on providing solutions that are appropriate for students' comprehending skills. To make this feasible, our faculty has offered RD Sharma Solutions exercise-by-exercise solutions for each chapter. When studying RD Sharma Class 12 Inverse Trigonometry Solutions, students should keep these tips and tricks in mind.

Before understanding the inverse of such functions, brush up on the fundamentals of trigonometric functions.
Students are recommended not to look at the solutions immediately when doing RD Sharma problems. Before solving, thoroughly read the question.
Solve the problems independently first, then match them to the RD Sharma Class 12 Maths Solutions Inverse Trigonometry.

Students can effortlessly prepare without missing any steps because Vedantu provides a step-by-step method to all the solutions. This also ensures that students understand all intermediate processes required to solve the problem. Students can take the extra practice and exercise problems to gain more subject knowledge on the concepts to perform outstandingly in the exam.

Let's take a closer look at some of the key concepts covered in this chapter:

Definition and meaning of inverse trigonometric functions
Inverse of sine(sin) function
Inverse of cosine(cos) function
Inverse of tangent(tan) function
Inverse of secant(sec) function
Inverse of cosecant(cosec) function
Inverse of cotangent(cot) function
Various properties of inverse trigonometric functions

Conclusion

Students will be more confident when studying through RD Sharma Class 12 Inverse Trigonometry Solutions. The solutions to every problem are designed carefully in a step-by-step manner so that students feel that they have covered all there bases on inverse trigonometry before sitting for their exams. Students can download free PDF available on Vedantu platform.

FAQs on RD Sharma Class 12 Maths Solutions Chapter 4 - Inverse Trigonometric Functions

1. What specific topics are covered in the RD Sharma Class 12 Maths Solutions for Chapter 4, Inverse Trigonometric Functions?

The solutions for RD Sharma Class 12 Chapter 4 provide comprehensive, step-by-step guidance on all key concepts. This includes the definition, domain, range, and principal value branches of all six inverse trigonometric functions, their graphs, and the application of their elementary properties to solve a wide variety of problems.

2. How does practising with RD Sharma solutions for Chapter 4 help in the CBSE board exam?

Practising with these solutions builds a strong foundation for the CBSE board exam. RD Sharma offers a wider range of problems than the NCERT textbook, including many Higher Order Thinking Skills (HOTS) questions. The detailed solutions help students master the methods needed to tackle any question type, ensuring they are well-prepared for the exam as per the 2025-26 syllabus.

3. What is the correct method to find the principal value of an inverse trigonometric function as shown in these solutions?

The solutions demonstrate the correct method which involves three main steps:

First, equate the given inverse trigonometric function to a variable, say 'y'.
Next, identify the specific range of the principal value branch for that function (e.g., [−π/2, π/2] for sin⁻¹x).
Finally, find the angle 'y' within that specific range that satisfies the trigonometric equation. This structured approach ensures answers are always correct according to CBSE guidelines.

4. How do these solutions help with solving Multiple Choice Questions (MCQs) on Inverse Trigonometric Functions?

The solutions are extremely useful for MCQs as they not only provide the correct answer but also explain the underlying properties and shortcuts. By understanding the step-by-step logic for complex problems, you can develop the speed and accuracy needed to solve MCQs effectively within the limited time of an exam.

5. Are the solutions for every single exercise in RD Sharma Class 12 Chapter 4 available?

Yes, the RD Sharma solutions for Chapter 4 are exhaustive. They cover every question from all the exercises within the chapter. Each problem is solved with a detailed, step-by-step explanation, ensuring that students can find a reliable method for any question they are struggling with.

6. Why is it so crucial to remember the specific range of principal value branches when solving problems?

Remembering the principal value branch is crucial because it ensures a unique and standard answer for any inverse trigonometric function. For instance, sin(x) = 0.5 has infinite solutions, but sin⁻¹(0.5) has only one principal value, π/6. The solutions consistently reinforce these ranges to help students avoid common errors in exams where only the principal value is accepted as the correct answer.

7. How do the RD Sharma solutions simplify complex problems that use properties like tan⁻¹x + tan⁻¹y?

The solutions break down complex problems by clearly identifying which property is being used at each stage. For a property like tan⁻¹x + tan⁻¹y, the solutions first state the formula, then check if the required conditions (like xy < 1) are met, and finally apply it step-by-step. This makes the simplification process logical and easy to replicate for similar problems.

8. What is a common mistake when simplifying expressions like cos(cos⁻¹x), and how do the solutions address this?

A common mistake is to assume cos(cos⁻¹x) is always 'x' without checking its value. This property only holds if 'x' is within the domain of cos⁻¹x, which is [-1, 1]. The RD Sharma solutions meticulously point this out, teaching students to first verify the domain and range constraints before applying any simplification formula, a critical habit for scoring full marks.

9. Can mastering Chapter 4 from RD Sharma solutions help in other advanced topics like Calculus?

Absolutely. A strong understanding of the properties and graphs of inverse trigonometric functions is a prerequisite for Calculus. The detailed methods in these solutions build a solid foundation that is directly applicable when you need to find the derivatives and integrals of inverse functions in later chapters, making those complex calculus problems much easier to solve.