Important Topics of Chapter 2
The following topics are covered in NCERT Chapter 2:
1. Meaning of Inverse Trigonometric Functions
2. Inverse of sine, cosine, tangent, cotangent, secant, and cosecant
3. Domain and range of inverse trigonometric functions
4. Principal value branch
5. Graphs of inverse trigonometric functions
6. Properties of inverse trigonometric functions
7. Relationship between trigonometric and inverse trigonometric functions
8. Simplification of expressions using inverse trigonometric functions
9. Solving equations involving inverse trigonometric functions
These topics are frequently asked in board exams and competitive exams.
Important Formulas – Chapter 2
Formulas are the backbone of this chapter. Students must learn and practice them regularly.
Basic Formulas
1. sin(sin⁻¹x) = x, where −1 ≤ x ≤ 1
2. cos(cos⁻¹x) = x, where −1 ≤ x ≤ 1
3. tan(tan⁻¹x) = x, where x ∈ ℝ
Properties of Inverse Trigonometric Functions
4. sin⁻¹(−x) = −sin⁻¹x
5. cos⁻¹(−x) = π − cos⁻¹x
6. tan⁻¹(−x) = −tan⁻¹x
Important Identity-Based Formulas
7. sin⁻¹x + cos⁻¹x = π/2
8. tan⁻¹x + cot⁻¹x = π/2
9. sec⁻¹x + cosec⁻¹x = π/2
Domain and Range (Very Important)
• Domain of sin⁻¹x and cos⁻¹x: −1 ≤ x ≤ 1
• Range of sin⁻¹x: −π/2 to π/2
• Range of cos⁻¹x: 0 to π
• Domain of tan⁻¹x: All real numbers
• Range of tan⁻¹x: −π/2 to π/2
Exercises in Chapter 2
NCERT Chapter 2 consists of 2 exercises only.
Exercise List
1. Exercise 2.1
2. Exercise 2.2
There is no miscellaneous exercise in this chapter.
Exercise 2.1 – Concept Building
This exercise focuses on:
• Basic understanding of inverse trigonometric functions
• Domain and range
• Principal value branch
Question Type:
• Find values
• True or false
• Simple evaluation
Exam Weightage: Useful for 1–2 mark questions
Exercise 2.2 – Simplification & Properties
This exercise includes:
• Simplification of expressions
• Proving identities
• Use of formulas
Question Type:
• Identity based questions
• Long answer type questions
Exam Weightage: Very important for 3–5 mark questions
Frequently Asked Questions (Long Answer Type – NCERT Based)
Q1. What are inverse trigonometric functions?
Inverse trigonometric functions are functions that give the angle whose trigonometric value is known. For example, sin⁻¹x gives the angle whose sine is x.
Q2. Why is domain restriction important in inverse trigonometric functions?
Trigonometric functions are not one-one over their complete domain. Domain restriction ensures that the inverse function gives only one value for each input.
Q3. What is the principal value branch?
The principal value branch is the restricted range of a trigonometric function where its inverse is defined uniquely.
Q4. Is sin⁻¹x equal to 1/sin x? Explain.
No. sin⁻¹x means inverse of sine, whereas 1/sin x is cosec x. Both are completely different.
Q5. Why is Chapter 2 important for calculus?
Inverse trigonometric functions are used in differentiation and integration, making this chapter very important for future topics.
Q6. Which inverse trigonometric function is defined for all real numbers?
tan⁻¹x is defined for all real numbers.
Q7. Are NCERT questions enough to score well in exams?
Yes, most board exam questions are directly or indirectly based on NCERT exercises.
Q8. What type of questions are frequently asked from this chapter?
Simplification, identity proofs, value finding, and domain-range based questions are frequently asked.
Q9. Is Chapter 2 easy to score?
Yes, it is a high-scoring and concept-based chapter if formulas are clear.
Q10. Where can students get complete NCERT solutions for Chapter 2?
Students can get free, detailed NCERT solutions, handwritten notes, and PDFs on Edu Tehri.
