Inverse Trigonometric Functions — Class 12 MCQs with Answers
Class 12 CBSE Mathematics · Chapter 2
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 12 CBSE Mathematics questions from Chapter 2, "Inverse Trigonometric Functions". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced apart.
To score well in "Inverse Trigonometric Functions", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Inverse Trigonometric Functions, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 12 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Inverse Trigonometric Functions (Class 12 Mathematics)
Trigonometric functions are made invertible by restricting each to a principal-value branch: sin⁻¹ and cos⁻¹ take domain [−1, 1], tan⁻¹ takes all of R. The chapter fixes these domains and ranges, drills standard principal values, and applies complementary, reciprocal, sum and double-angle identities to evaluate expressions.
- Principal value branch
- The restricted interval on which a trig function is one-one, so an inverse exists; sin⁻¹ uses [−π/2, π/2], cos⁻¹ uses [0, π].
- Domain of sin⁻¹, cos⁻¹
- Both are defined only for x ∈ [−1, 1], since sine and cosine never exceed 1 in magnitude.
- Range of sin⁻¹
- sin⁻¹x returns an angle in [−π/2, π/2]; this is why sin⁻¹(1/2) = π/6 and never 5π/6.
- Range of cos⁻¹
- cos⁻¹x returns an angle in [0, π]; it is never negative, so cos⁻¹(−1/2) = 2π/3.
Inverse Trigonometric Functions — important questions & MCQs with answers (Class 12 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Range of sin⁻¹x:
A.[0, π]B.[−π/2, π/2]✓ CorrectC.RD.[0, 2π]Answer: B. [−π/2, π/2]
Explanation: The principal-value branch restricts sin⁻¹x's output to [−π/2, π/2], not all of R — students confuse this with the domain [−1, 1], which is the input restriction, not the output.
- Q2Easy
Range of sin⁻¹ x:
A.[0, π]B.[−π/2, π/2]✓ CorrectC.[−π, π]D.RAnswer: B. [−π/2, π/2]
Explanation: sin⁻¹x's principal branch outputs only [−π/2, π/2] — half of cos⁻¹x's [0, π] range — because sine is one-to-one only on that restricted domain.
- Q3Easy
sin⁻¹(1/2) =
A.π/2B.π/4C.π/3D.π/6✓ CorrectAnswer: D. π/6
Explanation: sin 30° = sin(π/6) = 1/2, and π/6 sits inside the principal range [−π/2, π/2], so sin⁻¹(1/2) = π/6 — don't swap it with cos⁻¹(1/2) = π/3.
- Q4Easy
sin⁻¹ x + cos⁻¹ x =
A.π/2✓ CorrectB.πC.0D.π/4Answer: A. π/2
Explanation: sin⁻¹x and cos⁻¹x are complementary for every x in [−1, 1] — check x=0: sin⁻¹0 + cos⁻¹0 = 0 + π/2 = π/2, confirming the identity, never x or 0.
- Q5Easy
Domain of sin⁻¹x:
A.[−1, 1]✓ CorrectB.RC.[0,1]D.[−π,π]Answer: A. [−1, 1]
Explanation: Since sine only outputs values in [−1, 1], sin⁻¹x is defined only for x ∈ [−1, 1] — plugging in x = 2 has no real angle, unlike tan⁻¹x which accepts all of R.
- Q6Easy
Range of cos⁻¹ x:
A.[0, π]✓ CorrectB.[−π/2, π/2]C.[−π, π]D.RAnswer: A. [0, π]
Explanation: cos⁻¹x's principal branch is [0, π], not [−π/2, π/2] like sin⁻¹x — cosine is one-to-one on [0, π], which is why cos⁻¹(−1/2) = 2π/3, not a negative angle.
- Q7Medium
sin⁻¹(1/2) =
A.π/3B.π/6✓ CorrectC.π/4D.π/2Answer: B. π/6
Explanation: sin(π/6) = 1/2 and π/6 lies inside the principal range [−π/2, π/2], so sin⁻¹(1/2) = π/6 — not π/3, which is the angle for cos⁻¹(1/2) instead.
- Q8Medium
The principal value of sin⁻¹(−1/2) is:
A.−5π/6B.π/6C.7π/6D.−π/6✓ CorrectAnswer: D. −π/6
Explanation: Within [−π/2, π/2] the angle whose sine is −1/2 is −π/6.
- Q9Medium
sin⁻¹x + cos⁻¹x =
A.xB.πC.0D.π/2✓ CorrectAnswer: D. π/2
Explanation: sin⁻¹x and cos⁻¹x are complementary for every x ∈ [−1, 1]: e.g. sin⁻¹(1/2) + cos⁻¹(1/2) = π/6 + π/3 = π/2, never x or 0.
- Q10Medium
sin⁻¹(sin(2π/3)) =
A.π/3✓ CorrectB.2π/3C.π/6D.−π/3Answer: A. π/3
Explanation: 2π/3 lies outside [−π/2, π/2], so reflect using sin(π−x): sin(2π/3) = sin(π/3) = √3/2, and sin⁻¹(√3/2) = π/3 — not 2π/3 itself, a common trap.
- Q11Medium
The principal value of cos⁻¹(−1/2) is:
A.4π/3B.−π/3C.2π/3✓ CorrectD.π/3Answer: C. 2π/3
Explanation: Within [0, π] the angle whose cosine is −1/2 is 2π/3.
- Q12Hard
tan⁻¹ x + tan⁻¹ y = tan⁻¹((x+y)/(1−xy)) when:
A.NeverB.xy > 1C.AlwaysD.xy < 1✓ CorrectAnswer: D. xy < 1
Explanation: The direct tangent addition formula holds only when xy < 1, keeping the sum of the two angles inside (−π/2, π/2); for xy > 1 the +π term is needed instead.
- Q13Hard
The principal value of sin⁻¹(sin(3π/4)) is:
A.π/4✓ CorrectB.5π/4C.−π/4D.3π/4Answer: A. π/4
Explanation: 3π/4 lies outside [−π/2, π/2], and sin(3π/4) = sin(π/4), so the principal value is π/4.
- Q14Hard
tan⁻¹(1) + tan⁻¹(2) + tan⁻¹(3) =
A.π/2B.π✓ CorrectC.3π/2D.0Answer: B. π
Explanation: tan⁻¹1 = π/4; for tan⁻¹2+tan⁻¹3, since 2×3=6>1 the formula needs the +π term: π+tan⁻¹((2+3)/(1−6)) = π−π/4 = 3π/4. Adding π/4 gives π.
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Start this chapter free →Inverse Trigonometric Functions — FAQs
What are the key concepts in Class 12 Mathematics Inverse Trigonometric Functions?+
Trigonometric functions are made invertible by restricting each to a principal-value branch: sin⁻¹ and cos⁻¹ take domain [−1, 1], tan⁻¹ takes all of R. The chapter fixes these domains and ranges, drills standard principal values, and applies complementary, reciprocal, sum and double-angle identities to evaluate expressions. Key ideas include Principal value branch, Domain of sin⁻¹, cos⁻¹, Range of sin⁻¹, Range of cos⁻¹.
What does Class 12 Mathematics Chapter 2 (Inverse Trigonometric Functions) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Inverse Trigonometric Functions": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET 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 on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Inverse Trigonometric Functions" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Inverse Trigonometric Functions" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Inverse Trigonometric Functions" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip, the same negative marking as JEE Main and JEE Advanced. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Inverse Trigonometric Functions (Class 12 Mathematics)?+
The questions that matter most test Principal value branch, Domain of sin⁻¹, cos⁻¹, Range of sin⁻¹, Range of cos⁻¹. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Inverse Trigonometric Functions?+
Yes — Class 12 Mathematics Inverse Trigonometric Functions has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.