Check the below NCERT MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Inverse Trigonometric Functions Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Inverse Trigonometric Functions Class 12 MCQs Questions with Answers

Inverse Trigonometric Functions Class 12 MCQ Question 1.
sin-1 (sin$$\frac{2π}{3}$$) =
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{4π}{3}$$
(d) $$\frac{π}{3}$$

Answer: (d) $$\frac{π}{3}$$

Inverse Trigonometry Class 12 MCQ Question 2.
sin-1 (1 – x) – 2 sin-1 x = $$\frac{π}{2}$$ then x = ?
(a) 0, $$\frac{1}{2}$$
(b) 1, $$\frac{1}{2}$$
(c) $$\frac{1}{2}$$
(d) 0

MCQ Of Inverse Trigonometry Class 12 Question 3.
tan-1 √3 – sec-1(-2)
(a) π
(b) –$$\frac{π}{3}$$, 0
(c) $$\frac{π}{3}$$
(d) $$\frac{2π}{3}$$

Answer: (b) –$$\frac{π}{3}$$, 0

Inverse Trigonometric Functions MCQ Question 4.
sin(sec-1 x + cosec-1x) =
(a) 1
(b) -1
(c) $$\frac{π}{2}$$
(d) $$\frac{π}{3}$$

Class 12 Maths Chapter 2 MCQ Question 5.
2 tan-1 $$\frac{1}{3}$$ + tan-1 $$\frac{1}{7}$$ =
(a) tan-1 $$\frac{44}{29}$$
(b) $$\frac{π}{2}$$
(c) 0
(d) $$\frac{π}{4}$$

Answer: (d) $$\frac{π}{4}$$

MCQ On Inverse Trigonometric Functions Question 6.
The principle value of sin-1 $$\frac{√3}{2}$$ is
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{π}{4}$$
(d) $$\frac{π}{3}$$

Answer: (d) $$\frac{π}{3}$$

MCQ Inverse Trigonometry Class 12 Question 7.
The value of the expression tan-1($$\frac{1}{2}$$cos-1$$\frac{2}{√5}$$) is
(a) 2 + √5
(b) √5 – 2
(c) $$\frac{√5+2}{4}$$
(d) √5 + 2

Class 12 Inverse Trigonometry MCQ Question 8.
Simplified form of cos-1 (4x3 – 3x)
(a) 3 sin-1x
(b) 3 cos-1x
(c) π – 3 sin-1x
(d) None of these

Inverse Trigonometric Functions Class 12 MCQ With Solutions Question 9.
The value of tan(tan-1 $$\frac{4}{5}$$ + tan-1 $$\frac{2}{3}$$) is
(a) $$\frac{6}{17}$$
(b) $$\frac{7}{16}$$
(c) $$\frac{17}{6}$$
(d) None of these

MCQ On Inverse Trigonometric Functions Class 12 Question 10.
tan-1($$\frac{x}{y}$$) – tan-1($$\frac{x-y}{x+y}$$) is equal to
(a) $$\frac{π}{3}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{2}$$
(d) $$\frac{-3π}{4}$$

Answer: (b) $$\frac{π}{4}$$

Inverse Trigonometry MCQ Question 11.
The value of x for which sin |cot-1(1 – x)| = cos (tan-1 x) is
(a) $$\frac{2}{1}$$
(b) 1
(c) 0
(d) $$\frac{1}{2}$$

Answer: (d) $$\frac{1}{2}$$

Class 12 Maths Chapter 2 MCQ Questions Question 12.
Princal value of cos-1($$\frac{-1}{√2}$$)
(a) $$\frac{3π}{4}$$
(b) $$\frac{5π}{4}$$
(c) –$$\frac{π}{4}$$
(d) None of these

Answer: (a) $$\frac{3π}{4}$$

MCQ Questions For Inverse Trigonometry Class 12 With Solutions Question 13.
tan-1 √3 – sec-1 (-2) is equal to
(a) π
(b) –$$\frac{π}{3}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{2π}{3}$$

Answer: (b) –$$\frac{π}{3}$$

Class 12 Maths Ch 2 MCQ Question 14.
If y = sec-1 x then
(a) 0 ≤ y ≤ π
(b) 0 ≤ y ≤ $$\frac{π}{2}$$
(c) –$$\frac{π}{2}$$ < y < $$\frac{π}{2}$$
(d) None of these

Ch 2 Maths Class 12 MCQ Question 15.
If x + $$\frac{1}{x}$$ = 2 then the principal value of sin-1 x is x
(a) $$\frac{π}{4}$$
(b) $$\frac{π}{2}$$
(c) π
(d) $$\frac{3π}{2}$$

Answer: (d) $$\frac{3π}{2}$$

Inverse Trigonometry MCQ Class 12 Question 16.
4 tan-1 $$\frac{1}{5}$$ – tan-1 $$\frac{1}{239}$$
(a) π
(b) $$\frac{π}{2}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{4}$$

Answer: (d) $$\frac{π}{4}$$

Inverse Trigonometric Functions MCQ Pdf Question 17.
The principle value of sin-1(sin$$\frac{2π}{3}$$) is
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{-π}{6}$$
(d) $$\frac{π}{6}$$

Answer: (b) $$\frac{π}{3}$$

MCQ Questions For Inverse Trigonometry Class 12 Question 18.
The value of cos-1($$\frac{1}{2}$$) + 2sin-1($$\frac{1}{2}$$) is equal to
(a) $$\frac{π}{4}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{2π}{3}$$
(d) $$\frac{5π}{6}$$

Answer: (b) $$\frac{π}{6}$$

Chapter 2 Maths Class 12 MCQ Question 19.
Algebraic expression for sin (cot-1 x) is
(a) $$\frac{1}{1+x^2}$$
(b) $$\frac{1}{\sqrt{1+x^2}}$$
(c) $$\frac{x}{\sqrt{1+x^2}}$$
(d) None of these

Answer: (b) $$\frac{1}{\sqrt{1+x^2}}$$

Inverse Trigonometry MCQs Question 20.
If sin-1($$\frac{2x}{1+x^2}$$) + sin-1$$\frac{2y}{1+y^2}$$ = 2 tan-1 a then a is equal to
(a) $$\frac{x-y}{1+xy}$$
(b) $$\frac{y}{1+xy}$$
(c) $$\frac{y}{1-xy}$$
(d) $$\frac{x+y}{1-xy}$$

Answer: (d) $$\frac{x+y}{1-xy}$$

Question 21.
Princal value of tan-1 (-1) is
(a) $$\frac{π}{4}$$
(b) $$\frac{-π}{2}$$
(c) $$\frac{5π}{4}$$
(d) $$\frac{-π}{4}$$

Answer: (d) $$\frac{-π}{4}$$

Question 22.
tan-1($$\frac{1}{4}$$) + tan-1($$\frac{2}{9}$$) equal to

Answer: (d) tan-1($$\frac{1}{2}$$)

Question 23.
Principal value of sin-1($$\frac{1}{√2}$$)
(a) $$\frac{π}{4}$$
(b) $$\frac{3π}{4}$$
(c) $$\frac{5π}{4}$$
(d) None of these

Answer: (a) $$\frac{π}{4}$$

Question 24.
sin-1 x = y Then
(a) 0 ≤ y ≤ π
(b) –$$\frac{π}{2}$$ ≤ y ≤ $$\frac{π}{2}$$
(c) 0 < y < π
(d) –$$\frac{π}{2}$$ < y < –$$\frac{π}{2}$$

Answer: (b) –$$\frac{π}{2}$$ ≤ y ≤ $$\frac{π}{2}$$

Question 25.
cos-1(cos$$\frac{7π}{6}$$) is equal to
(a) $$\frac{7π}{6}$$
(b) $$\frac{5π}{6}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{6}$$

Answer: (b) $$\frac{5π}{6}$$

Question 26.
sin[$$\frac{π}{3}$$ – sin-1(-$$\frac{1}{2}$$)] is equal to
(a) $$\frac{1}{2}$$
(b) $$\frac{1}{3}$$
(c) $$\frac{1}{4}$$
(d) 1

Question 27.
tan-1$$\frac{1}{2}$$ + tan-1$$\frac{2}{11}$$ = tan-1 a then a = ?
(a) $$\frac{1}{4}$$
(b) $$\frac{1}{2}$$
(c) $$\frac{3}{4}$$
(d) 1

Answer: (c) $$\frac{3}{4}$$

Question 28.
tan-1$$\frac{1}{2}$$ + tan-1$$\frac{1}{3}$$ =
(a) $$\frac{π}{4}$$
(b) $$\frac{π}{2}$$
(c) $$\frac{π}{3}$$
(d) π

Answer: (a) $$\frac{π}{4}$$

Question 29.
If sin-1 x + sin-1 y = $$\frac{2π}{3}$$ then cos-1 x + cos-1 y =
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{2}$$

Answer: (c) $$\frac{π}{3}$$

Question 30.
The principal value of cosec-1 (-2) is
(a) –$$\frac{2π}{3}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{2π}{3}$$
(d) –$$\frac{π}{6}$$

Answer: (d) –$$\frac{π}{6}$$

Question 31.
The domain of the following f(x) = $$\sqrt{sin^{-1}x}$$ is
(a) [0, 1]
(b) [-1, 1]
(c) [-, 0]
(d) [0, 1]

Question 32.
Which of the following is the principal value branch of cos-1 x?
(a) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$]
(b) (0, π)
(c) (0, π)
(d) (0, π) – {$$\frac{π}{2}$$}

Question 33.
Which of the following is the principal value branch of cosec-1 x?
(a) ($$\frac{-π}{2}$$, $$\frac{π}{2}$$)
(b) (0, π) – {$$\frac{π}{2}$$}
(c) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$]
(d) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$] – [0]

Answer: (d) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$] – [0]

Question 34.
If 3 tan-1 x + cot-1 x = π, then x equals
(a) 0
(b) 1
(c) -1
(d) $$\frac{1}{2}$$

Question 35.
The value of cos-1[cos($$\frac{33π}{5}$$)] is
(a) $$\frac{3π}{5}$$
(b) $$\frac{-3π}{5}$$
(c) $$\frac{π}{10}$$
(d) –$$\frac{-π}{10}$$

Answer: (a) $$\frac{3π}{5}$$

Question 36.
The domain of the function cos-1 (2x – 1) is
(a) [0, 1]
(b) [-1, 1]
(c) [-1, -1]
(d) [0, π]

Question 37.
The domain of the function defined by f (x) = sin-1 $$\sqrt{x-1}$$ is
(a) [1, 2]
(b) [-1, 1]
(c) [0, 1]
(d) None of these

Question 38.
If cos(sin-1$$\frac{2}{5}$$ + cos-1 x) = 0 then x is equal to
(a) $$\frac{1}{5}$$
(b) $$\frac{2}{5}$$
(c) 0
(d) 1

Answer: (b) $$\frac{2}{5}$$

Question 39.
The value of sin (2 tan-1 (.75)) is equal to
(a) .75
(b) 1.5
(c) .96
(d) sin 1.5

Question 40.
The value of cos-1 (cos$$\frac{3π}{2}$$) is equal to
(a) $$\frac{π}{2}$$
(b) $$\frac{3π}{2}$$
(c) $$\frac{5π}{2}$$
(d) –$$\frac{7π}{2}$$

Answer: (a) $$\frac{π}{2}$$

Question 41.
The value of expression 2 sec-1 2 + sin-1 ($$\frac{1}{2}$$) is
(a) $$\frac{π}{6}$$
(b) $$\frac{5π}{6}$$
(c) $$\frac{7π}{6}$$
(d) 1

Answer: (b) $$\frac{5π}{6}$$

Question 42.
If tan-1 x + tan-1 y = $$\frac{4π}{5}$$ then cot-1 x + cot-1 y equals
(a) $$\frac{π}{5}$$
(b) $$\frac{2π}{5}$$
(c) $$\frac{3π}{5}$$
(d) π

Answer: (a) $$\frac{π}{5}$$

Question 43.
If sin-1($$\frac{2a}{1+a^2}$$) + cos-1($$\frac{1-a^2}{1+a^2}$$) = tan-1($$\frac{2x}{1-x^2}$$) where a, x ∈ |0, 1| then the value of x is
(a) 0
(b) $$\frac{a}{2}$$
(c) a
(d) $$\frac{2a}{1-a^2}$$

Answer: (d) $$\frac{2a}{1-a^2}$$

Question 44.
The value of sin [cos-1($$\frac{7}{25}$$)] is
(a) $$\frac{25}{24}$$
(b) $$\frac{25}{7}$$
(c) $$\frac{24}{25}$$
(d) $$\frac{7}{24}$$

Answer: (c) $$\frac{24}{25}$$

Question 45.
If |x| ≤ 1, then 2 tan-1 x + sin-1($$\frac{2x}{1+x^2}$$) is equal to
(a) 4 tan-1 x
(b) $$\frac{π}{2}$$
(c) 0
(d) π

Question 46.
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

Question 47.
The number of real solution of the equation is
$$\sqrt{1+cos 2x}$$ = √2 cos-1(cos x) in [$$\frac{π}{2}$$, π] is
(a) 0
(b) 1
(c) 2
(d) None of these

Question 48.
If cos-1 x > sin-1 x, then
(a) $$\frac{1}{√2}$$ < x ≤ 1
(b) 0 ≤ x < $$\frac{1}{√2}$$
(c) -1 ≤ x < $$\frac{1}{√2}$$ (d) x > 0

Answer: (b) 0 ≤ x < $$\frac{1}{√2}$$

Question 49.
sin-1($$\frac{-1}{2}$$)
(a) $$\frac{π}{3}$$
(b) –$$\frac{π}{3}$$
(c) $$\frac{π}{6}$$
(d) –$$\frac{π}{6}$$

Answer: (d) –$$\frac{π}{6}$$

Question 50.
sec-1($$\frac{-2}{√3}$$)
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{5π}{6}$$
(d) –$$\frac{2π}{3}$$

Answer: (c) $$\frac{5π}{6}$$

Question 51.
cos-1($$\frac{1}{2}$$)
(a) –$$\frac{π}{3}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{π}{2}$$
(d) $$\frac{2π}{3}$$

Answer: (b) $$\frac{π}{3}$$

Question 52.
cosec-1($$\frac{-2}{√3}$$)
(a) –$$\frac{π}{3}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{π}{2}$$
(d) –$$\frac{π}{2}$$

Answer: (a) –$$\frac{π}{3}$$

Question 53.
cot-1(1)
(a) $$\frac{π}{3}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{2}$$
(d) 0

Answer: (b) $$\frac{π}{4}$$

Question 54.
cos-1($$\frac{√3}{2}$$)
(a) $$\frac{5π}{6}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{4π}{9}$$
(d) $$\frac{2π}{3}$$

Answer: (a) $$\frac{5π}{6}$$

Question 55.
cosec-1(2)
(a) $$\frac{π}{6}$$
(b) $$\frac{2π}{3}$$
(c) $$\frac{5π}{6}$$
(d) 0

Answer: (a) $$\frac{π}{6}$$

Question 56.
sec-1(2)
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{2π}{3}$$
(d) $$\frac{5π}{6}$$

Answer: (b) $$\frac{π}{3}$$

Question 57.
tan-1(√3)
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{2π}{3}$$
(d) $$\frac{5π}{6}$$

Answer: (b) $$\frac{π}{3}$$

Question 58.
cot-1(-√3)
(a) $$\frac{5π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{π}{2}$$
(d) $$\frac{π}{4}$$

Answer: (a) $$\frac{5π}{6}$$

Question 59.
tan-1 + cos-1 ($$\frac{-1}{2}$$) + sin-1 ($$\frac{-1}{2}$$)
(a) $$\frac{2π}{3}$$
(b) $$\frac{3π}{4}$$
(c) $$\frac{π}{2}$$
(d) 6π

Answer: (b) $$\frac{3π}{4}$$

Question 60.
tan-1 (√3) + sec-1 (-2) – cosec-1 ($$\frac{2}{√3}$$)
(a) $$\frac{5π}{6}$$
(b) $$\frac{2π}{3}$$
(c) $$\frac{π}{3}$$
(d) 0

Question 61.
cos-1 ($$\frac{-1}{2}$$) + 2sin-1 ($$\frac{-1}{2}$$)
(a) $$\frac{π}{3}$$
(b) $$\frac{2π}{3}$$
(c) $$\frac{3π}{4}$$
(d) $$\frac{5π}{8}$$

Answer: (a) $$\frac{π}{3}$$

Question 62.
If cot-1 ($$\sqrt{cosα}$$) – tan-1 ($$\sqrt{cosα}$$) = x then sin x is equal to
(a) tan² ($$\frac{α}{2}$$)
(b) cot² ($$\frac{α}{2}$$)
(c) tan α
(d) cot ($$\frac{α}{2}$$)

Answer: (a) tan² ($$\frac{α}{2}$$)

Question 63.
4 tan-1 $$\frac{1}{5}$$ – tan-1 $$\frac{1}{70}$$ + tan-1 $$\frac{1}{99}$$ is equal to
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{2}$$

Answer: (b) $$\frac{π}{4}$$

Question 64.
If 6 sin-1 (x² – 6x + 8.5) = π, then x is equal to
(a) 1
(b) 2
(c) 3
(d) 8

Question 65.
Number of solutions of the equation
tan-1 ($$\frac{1}{2x+1}$$) + tan-1 ($$\frac{1}{4x+1}$$) = tan-1 ($$\frac{2}{x^2}$$)
(a) 1
(b) 2
(c) 3
(d) 4
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