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

Questions
1 The value of cos-1[cos(33π/5)] is
A 3π/5
B −3π/5
C π/10
D –−π/10

Answer:3π/5
2 The value of cos-1 (cos 3π/2) is equal to
A π/2
B 3π/2
C 5π/2
D –7π/2

Answer:π/2

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3 If sin-1 Inverse Trigonometric Functions where a, x ∈ |0, 1| then the value of x is
A 0
B a/2
C a
D 2a/1−a2

Answer:2a/1−a2
4 The number of real solution of the equation is

√2cos-1(cos x) in [π/2, π] is

A 0
B 1
C 2
D None of these

Answer:2
5 sec-1(−2/√3)
A π/6
B π/3
C 5π/6
D –2π/3

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

Answer:–π/3
7 sec-1(2)
A π/6
B π/3
C 2π/3
D 5π/6

Answer:π/3
8 tan-1 + cos-1 (−1/2) + sin-1 (−1/2)
A 2π/3
B 3π/4
C π/2
D 6/π

Answer:3π/4
9 cos-1 (−1/2) + 2sin-1 (−1/2)
A π/3
B 2π/3
C 3π/4
D 5π/8

Answer:π/3
10 If cot-1 (√cosα) – tan-1 (√cosα) = x then sin x is equal to
A tan² (α/2)
B cot² (α/2)
C tan α
D cot (α/2)

Answer:tan² (α/2)
11 If sin(πcot x) = cos(πtan x), then cot 2x is equals to
A n - 1/4
B n + 1/4
C 4n + 1
D 4n - 1

Answer:n + 1/4
12 The value of sin{2 sin-1 (0.8)} is
A 1
B 0.96
C 0.80
D none of these

Answer:0.96
13 If x + 1/x = 2, then the principle value of cos-1 x is
A π
B 3π/2
C π/2
D 0

Answer:0
14 sin{sin-1 (1/2) + cos-1 (1/2)} is equals to
A 0
B 1
C -1
D 2

Answer:1
15 If π/2 ≤ x ≤ 3π/2, then sin-1 (sin x) is equals to
A π
B x
C π - x
D π + x

Answer:π - x
16 If r2 = x2 + y2 + z2 then tan-1 (yz/xr) + tan-1 (xz/yr) + tan-1 (xy/zr) is equals to
A π/4
B π/3
C π/2
D None of these

Answer:π/2
17 If tan-1 (a/x) + tan-1 (a/x) = π/2, the x =
A √a
B √b
C √ab
D none of these

Answer:√ab
18 The value of tan-1 (1/3) + tan-1 (1/5) + tan-1 (1/7) + tan-1 (1/8) is
A π/4
B π/3
C π/2
D None of these

Answer:π/4
19 If cos 20 = k and cos x = 2k2 - 1, then the possible values of x between 0 and 360 degrees are
A 140 degree
B 40 degree and 140 degree
C 40 degree and 320 degree
D 50 degree and 130 degree

Answer:40 degree and 320 degree
20 Domain of the function f (x) = sin-1 x is
A [0,1]
B R
C [ -1, 1]
D none of these

Answer:[ -1, 1]

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