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NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

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NCERT Maths Chapter 2 Inverse Trigonometric Functions Solutions of Class 12 - Free PDF Download

NCERT Solutions for Class 12 Maths Chapter 2 Solutions PDF is available for download. You can find the official PDF on Vedantu's website and download it from there. The Inverse Trigonometric Functions Class 12 PDF complete solutions have been provided for Chapter 2 of Class 12 NCERT Maths. A learner can find anything and everything related to Class 12 Maths Chapter 2. Vedantu has a team of passionate and devoted educators who are ready to depart their knowledge and expertise in the most effective way possible. In addition to this, if a student faces any doubts concerning CH 2 Maths Class 12, he or she can go to the website and drop in their queries and download NCERT Book Solution for Class 12 Maths Chapter 2 solutions PDF. They will get back to you in case of doubts and clear that off in a very efficient manner.

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Practice and Master the Concepts of Real Numbers with NCERT Solutions Ex for Class 12 Maths

Exercise 2.1: In this exercise, students will learn about the inverse trigonometric functions, including their domain, range, and principal values. They will also practice finding the inverse trigonometric functions of various values and solving equations involving inverse trigonometric functions.


Exercise 2.2: This exercise focuses on the properties of inverse trigonometric functions. Students will learn about the properties of sine, cosine, tangent, cotangent, secant, and cosecant functions, and practice using these properties to evaluate inverse trigonometric functions.


Importance of Inverse Trigonometric Functions

In the fields of engineering, construction, and architecture, inverse trigonometric ratios are widely used. Inverse trigonometric ratios are the easiest way to find an unknown angle, therefore we utilize them in places where we need to know the angle for our help and quickly get the correct values. 


The following are a few examples of inverse trigonometric ratios in use.


  • A right-angled triangle's unknown angles are measured using this formula.

  • Used to determine the angle of inclination or depression. 

  • It is used by architects to measure the angle of a bridge and its supports.

  • Carpenters use this to achieve a particular cut angle.


Overview of Deleted Syllabus for CBSE Class 12 Maths Chapter 2 Inverse Trigonometric Functions

Chapter

Dropped Topics

Inverse Trigonometric Functions

2.3 Properties of Inverse Trigonometric Functions (Except sin (sin-1 x) = x, x ∈ [-1, 1] sin-1 (sin x) = x, x ∈ [-π/2, π/2]

Page Number 45 – 47 

Examples 4, 7 and 8

Alternative Solution of Example 5

Page Number 47- 48:
Questions - 3, 4, 6, 12, 14, 15

Page Number 49-51

Examples 10, 11, 12, 13

Page 51-52 Miscellaneous Exercise

Question number - 8, 12, 17

Page 53 Summary Points from 8 to 13


Class 12 Maths NCERT Solutions Chapter 2 All Exercises

Exercise

Number of Questions

Exercise 2.1 Solutions

14 Questions & Solutions (14 Short Answers)

Exercise 2.2 Solutions

20 Questions & Solutions (4 Short Answers, 16 Long Answers)


Other Study Materials of CBSE Class 12 Maths Chapter 2


NCERT Solutions for Class 12 Maths | Chapter-wise List

Given below are the chapter-wise NCERT 12 Maths solutions PDF. Using these chapter-wise class 12th maths ncert solutions, you can get clear understanding of the concepts from all chapters.



Related Links for NCERT Class 12 Maths in Hindi

Explore these essential links for NCERT Class 12 Maths in Hindi, providing detailed solutions, explanations, and study resources to help students excel in their mathematics exams.



Important Related Links for NCERT Class 12 Maths

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FAQs on NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

1. What is the correct stepwise method to solve questions in NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions?

To solve questions from NCERT Solutions for Class 12 Maths Chapter 2, follow these CBSE-recommended steps:

  • Identify the type of inverse trigonometric function involved and note its principal value branch.
  • Simplify the given expression using standard identities or algebraic manipulation as per NCERT patterns.
  • Substitute any known values and maintain the stepwise justification for each transformation, especially where domain or range restrictions apply.
  • Write the final answer, clearly highlighting the principal value and method, as expected in the CBSE examination.

2. Why is mentioning the principal value crucial when solving inverse trigonometric function problems as per NCERT Solutions?

The principal value is crucial because each inverse trigonometric function is defined within a specific range, called its principal branch. NCERT and CBSE mark schemes award full marks only when answers specify the correct principal value, reflecting precise mathematical understanding and stepwise methodology.

3. How do NCERT Solutions for Class 12 Maths Chapter 2 help in tackling complex identities involving sine, cosine, or tangent inverses?

These solutions provide a step-by-step breakdown for each identity-based question, illustrating each transformation, such as domain checks and value substitutions. By following CBSE pattern answers, students learn to justify every step, which is essential for scoring well in board exams involving inverse trigonometric identities.

4. What are some common mistakes students should avoid when following NCERT Solutions for Inverse Trigonometric Functions?

Key errors to avoid include:

  • Missing the principal value restriction and writing angles outside the specified range.
  • Incorrectly applying identities without verifying the domain or argument value.
  • Skipping intermediate steps, which is penalized in CBSE marking.
  • Ignoring the required stepwise answer format prescribed by NCERT and CBSE.

5. How can Hindi medium students ensure their answers align with CBSE guidelines for this chapter?

Hindi medium students should ensure each step in their solution follows the NCERT textbook structure, uses proper mathematical terminology, and includes principal values. Writing answers in a clear, stepwise manner as per CBSE 2025–26 expectations guarantees alignment and maximum marks.

6. What role do stepwise NCERT Solutions play in improving answer writing for the Miscellaneous Exercise in Chapter 2?

Stepwise NCERT Solutions serve as a model showing how to structure each answer logically. By studying the detailed solutions, students understand how to proceed from one step to the next, ensure justification for each calculation, and meet all the points considered in CBSE's marking scheme for the Miscellaneous Exercise.

7. In what ways can understanding the properties of inverse trigonometric functions aid in solving Exam Exercise 2.2?

Mastery over properties helps students:

  • Quickly transform complex expressions into simplified forms.
  • Correctly interchange between different inverse trigonometric forms, such as using identities to switch between arcsin and arccos.
  • Address questions involving similarity or reduction to principal values, as required for full marks in NCERT Exercise 2.2.

8. How can practicing with Class 12 NCERT Solutions for Inverse Trigonometric Functions strengthen time management in CBSE board exams?

Practicing stepwise solutions trains students to break down each problem into logical steps, reducing confusion during the exam. Familiarity with the expected answer pattern also reduces errors, helping students attempt all questions confidently and within time limits.

9. How does the NCERT Solutions methodology help address real-life applications of inverse trigonometric functions?

By presenting solutions in a concept-based, stepwise manner, NCERT Solutions build an understanding of how inverse trigonometric functions are used to calculate angles in engineering, architecture, and physics. This approach bridges textbook learning with practical scenarios, deepening conceptual grasp for both academic and applied contexts.

10. If my answer format differs slightly from the NCERT stepwise method, will it impact my score in CBSE exams?

Yes, CBSE marking schemes give preference to answers formatted as per NCERT guidelines. Following the stepwise, justified approach with clear mention of principal values and all intermediate steps is essential. Diverging from this may result in partial or no marks, even if the final value is correct.