NCERT Solutions for class 12 Maths | Chapter 2 - Inverse Trigonometric Functions

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Questions
1 tan-1 (√3) + sec-1 (-2) – cosec-1 (2/√3)
A 5/π
B 2π/3
C π/3
D 0

Answer:0
2 The principle value of sin-1(sin2π/3)is
A 2π/3
B π/3
C -π/6
D π/6

Answer:π/3
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3 Algebraic expression for sin (cot-1 x) is
A 1/1+x2
B
C
D None of these

Answer:
4 cos-1(cos7π/6) is equal to
A 7π/6
B 5π/6
C π/3
D π/6

Answer:5π/6
5 cosec-1(2)
A π/6
B 2π/3
C 5π/6
D 0

Answer:π/6
6 If 6 sin-1 (x² – 6x + 8.5) = π, then x is equal to
A 1
B 2
C 3
D 8

Answer:2
7 tan-1 √3 – sec-1(-2)
A π
B –π/3, 0
C π/3
D 2π/3

Answer:–π/3, 0
8 sin(sec-1 x + cosec-1x) =
A 1
B -1
C π/2
D π/3

Answer:1
9 sin-1 (1 – x) – 2 sin-1 x = π/2 then x = ?
A 0, 1/2
B 1, 1/2
C 1/2
D 0

Answer:0
10 The value of x for which sin |cot-1(1 – x)| = cos (tan-1 x) is
A 2/1
B 1
C 0
D 1/2

Answer:1/2
11 Simplified form of cos-1 (4x3 – 3x)
A 3 sin-1x
B 3 cos-1x
C π – 3 sin-1x
D None of these

Answer:3 cos-1x
12 4 tan-1 15 – tan-1 1/239
A π
B π/2
C π/3
D π/4

Answer:π/4
13 Principal value of sin-1(1√2)
A π/4
B 3π/4
C 5π/4
D None of these

Answer:π/4
14 The principal value of cosec-1 (-2) is
A –2π/3
B π/6
C 2π/3
D –π/6

Answer:–π/6
15 Which of the following is the principal value branch of cos-1 x?
A [−π/2, π/2]
B (0, π)
C (0, π)
D (0, π) – {π/2}

Answer:(0, π)
16 If 3 tan-1 x + cot-1 x = π, then x equals
A 0
B 1
C -1
D 1/2

Answer:1
17 The domain of the function cos-1 (2x – 1) is
A [0, 1]
B [-1, 1]
C [-1, -1]
D [0, π]

Answer:[0, 1]
18 If tan-1 x + tan-1 y = 4π5 then cot-1 x + cot-1 y equals
A π/5
B 2π/5
C 3π/5
D π

Answer:π/5
19 If cos-1 α + cos-1 β + cos-1 γ = 3π, then α(β + γ) + β (γ + α) + γ(α + β) equals
A 0
B 1
C 6
D 12

Answer:6
20 If cos-1 x > sin-1 x, then
A 1/√2 < x ≤ 1
B 0 ≤ x < 1/√2
C -1 ≤ x < 1/√2
D x > 0

Answer:0 ≤ x < 1/√2

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