Class 12 Maths Chapter 2: Inverse Trigonometric Functions MCQs with answers
10 multiple-choice questions on Inverse Trigonometric Functions, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.
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Answer: (b) cot⁻¹
cot⁻¹ : R → (0, π). cos⁻¹ has the closed range [0, π]; sec⁻¹ has [0, π] − {π/2}, which contains 0 and π; tan⁻¹ has (−π/2, π/2).
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Answer: (b) R − (−1, 1)
cosec x takes every real value except those strictly between −1 and 1, so its inverse is defined on R − (−1, 1).
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Answer: (c) cosec x
(sin x)⁻¹ is the reciprocal 1/sin x = cosec x. It must not be confused with sin⁻¹ x, the inverse function.
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Answer: (a) −π/6
Principal values of cos⁻¹ lie in [0, π]. 0 = cos⁻¹ 1, π = cos⁻¹(−1) and 5π/6 = cos⁻¹(−√3/2) are attained; −π/6 lies outside [0, π].
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Answer: (c) 2π/5
The range of tan⁻¹ is the open interval (−π/2, π/2): the end points ±π/2 are never reached. Of the four, only 2π/5 lies strictly inside it.
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Answer: (b) −π/3
x = cos(5π/6) = −√3/2. sin⁻¹(−√3/2) must lie in [−π/2, π/2], and sin(−π/3) = −√3/2, so sin⁻¹ x = −π/3.
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Answer: (c) −√3
5π/6 lies in (0, π), so x = cot(5π/6) = −cot(π/6) = −√3.
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Answer: (d) −√2
3π/4 lies in [0, π] − {π/2}, so x = sec(3π/4) = 1/cos(3π/4) = 1/(−1/√2) = −√2.
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Answer: (b) [1/3, 1]
sin⁻¹ is defined on [−1, 1]: −1 ≤ 3x − 2 ≤ 1 gives 1 ≤ 3x ≤ 3, that is 1/3 ≤ x ≤ 1.
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Answer: (c) (−∞, −1] ∪ [0, ∞)
sec⁻¹ is defined on R − (−1, 1): 2x + 1 ≤ −1 or 2x + 1 ≥ 1, so x ≤ −1 or x ≥ 0. The end points are included, since sec⁻¹(−1) = π and sec⁻¹(1) = 0.