Class 12 Mathematics — Chapter 2: Inverse Trigonometric Functions
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 2, "Inverse Trigonometric Functions", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Inverse Trigonometric Functions" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Inverse Trigonometric Functions, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.
Key concepts: Inverse Trigonometric Functions (Class 12 Mathematics)
This chapter defines the inverse trigonometric functions on their principal-value branches and develops their key properties and identities.
- Need for restriction
- Trigonometric functions are not one-one over all reals, so their domains are restricted to define inverses with unique principal values.
- Principal value branches
- e.g. sin⁻¹x ∈ [−π/2, π/2], cos⁻¹x ∈ [0, π], tan⁻¹x ∈ (−π/2, π/2).
- Complementary identities
- sin⁻¹x + cos⁻¹x = π/2; tan⁻¹x + cot⁻¹x = π/2; sec⁻¹x + cosec⁻¹x = π/2.
- Negative-argument rules
- sin⁻¹(−x) = −sin⁻¹x, tan⁻¹(−x) = −tan⁻¹x, but cos⁻¹(−x) = π − cos⁻¹x.
- Sum formula
- tan⁻¹x + tan⁻¹y = tan⁻¹[(x + y)/(1 − xy)], valid when xy < 1.
Key formulas — Inverse Trigonometric Functions
💡 Exam tips for Inverse Trigonometric Functions
- Always give answers within the principal-value branch — that is what 'inverse function' means here.
- Watch the condition xy < 1 in the tan⁻¹ sum formula; otherwise add or subtract π.
Sample questions
Range of sin⁻¹x:
Principal value branch.
sin⁻¹(1/2) =
sin(π/6) = 1/2.
tan⁻¹(1) + tan⁻¹(2) + tan⁻¹(3) =
Classic identity.
Inverse Trigonometric Functions — FAQs
What are the key concepts in Class 12 Mathematics Inverse Trigonometric Functions?+
This chapter defines the inverse trigonometric functions on their principal-value branches and develops their key properties and identities. Key ideas include Need for restriction, Principal value branches, Complementary identities, Negative-argument rules, Sum formula.
What does Class 12 Mathematics Chapter 2 (Inverse Trigonometric Functions) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Inverse Trigonometric Functions" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.
Are these "Inverse Trigonometric Functions" questions free to practise?+
Yes — sign in with Google to practise "Inverse Trigonometric Functions" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Inverse Trigonometric Functions" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
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