# MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers

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## Inverse Trigonometric Functions Class 12 MCQs Questions with Answers

Don’t forget to practice the multitude of MCQ Questions on Inverse Trigonometric Functions Class 12 with answers so you can apply your skills during the exam.

Question 1.
If sin-1 x + sin-1 y = $$\frac { 2π }{3}$$, then the value of cos-1 x + cos-1 y is
(a) $$\frac { 2π }{3}$$
(b) $$\frac { π }{3}$$
(c) $$\frac { π }{2}$$
(d) π

Answer: (b) $$\frac { π }{3}$$

Question 2.
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) –$$\frac { π }{3}$$

Question 3.
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 4.
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 5.
tan-1 √3 – cot-1(-√3) is equal to
(a) π
(b) –$$\frac { π }{2}$$
(c) 0
(d) 2√3

Answer: (b) –$$\frac { π }{2}$$

Question 6.
sin (tan-1 x), |x| < 1, is equal to
(a) $$\frac { x }{\sqrt{1-x^2}}$$
(b) $$\frac { 1 }{\sqrt{1-x^2}}$$
(c) $$\frac { x }{\sqrt{1+x^2}}$$
(d) $$\frac { x }{\sqrt{1+x^2}}$$

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

Question 7.
sin-1 (1 – x) – 2 sin-1 x = $$\frac { π }{2}$$, then x is equal to
(a) 0, $$\frac { 1 }{2}$$
(b) 1, $$\frac { 1 }{2}$$
(c) 0
(d) $$\frac { 1 }{2}$$

Question 8.
tan-1 ($$\frac { x }{y}$$) – tan-1 $$\frac { x-y }{x+y}$$ is equal to
(a) $$\frac { π }{2}$$
(b) $$\frac { π }{3}$$
(c) $$\frac { π }{4}$$
(d) –$$\frac { 3π }{4}$$

Answer: (c) $$\frac { π }{4}$$

Question 9.
The value of sin-1(cos($$\frac { 43π }{5}$$)) is
(a) $$\frac { 3π }{5}$$
(b) $$\frac { -7π }{5}$$
(c) $$\frac { π }{10}$$
(d) –$$\frac { -π }{10}$$

Answer: (d) –$$\frac { -π }{10}$$

Question 10.
The principal value of the expression
cos-1 [cos (-680°)] is
(a) $$\frac { 2π }{9}$$
(b) $$\frac { -2π }{9}$$
(c) $$\frac {34π }{9}$$
(d) –$$\frac { π }{9}$$

Answer: (a) $$\frac { 2π }{9}$$

Question 11.
The value of cot (sin-1x) is
(a) $$\frac { \sqrt{1+x^2} }{x}$$
(b) $$\frac { x }{\sqrt{1+x^2}}$$
(c) $$\frac {1}{x}$$
(d) $$\frac { \sqrt{1-x^2} }{x}$$

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

Question 12.
The domain of sin-1 2x is
(a) [0, 1]
(b) [-1, 1]
(c) [$$\frac {-1}{2}$$, $$\frac {1}{2}$$]
(d) [-2, 2]

Answer: (c) [$$\frac {-1}{2}$$, $$\frac {1}{2}$$]

Question 13.
The greatest and least values of (sin-1 x)² + (cos-1x)² are respectively
(a) $$\frac { 5π^2 }{4}$$ and $$\frac { π^2 }{8}$$
(b) $$\frac { π }{2}$$ and $$\frac { -π }{2}$$
(c) $$\frac { π^2 }{4}$$ and $$\frac { -π^2 }{4}$$
(d) –$$\frac { π^2 }{4}$$ and 0

Answer: (a) $$\frac { 5π^2 }{4}$$ and $$\frac { π^2 }{8}$$

Question 14.
If cos-1 x – cos-1 — = α, then 4x² – 4xy cos α + y² is equal to:
(a) 4
(b) 2 sin² α
(c) -4 sin² α
(d) 4 sin² α.

Hint:

Squaring, 4x² + y² cos² α – 4xy cos α
= 4 sin² α – y² sin² α
⇒ 4x² – 4xy cos α + y² = 4 sin² α.

Question 15.
If sin-1 ($$\frac {5}{4}$$) = $$\frac {π}{2}$$, then the value of x is
(a) 3
(b) 4
(c) 5
(d) 1

Hint:

Question 16.
The value of cot (cosec-1$$\frac {5}{3}$$ + tan-1$$\frac {2}{3}$$) is
(a) $$\frac { 5 }{17}$$
(b) $$\frac { 6 }{17}$$
(c) $$\frac { 3 }{17}$$
(d) $$\frac { 4 }{17}$$

Answer: (b) $$\frac { 6 }{17}$$
Hint:

Question 17.
If tan-1 y = tan-1 x + tan-1($$\frac { 2x }{1-x^2}$$) when |x| < $$\frac { 1 }{√3}$$, then the value of y is:
(a) $$\frac { 3x-x^3 }{1-3x^2}$$
(b) $$\frac { 3x+x^3 }{1-3x^2}$$
(c) $$\frac { 3x-x^3 }{1+3x^2}$$
(d) $$\frac { 3x+x^3 }{1+3x^2}$$

Answer: (a) $$\frac { 3x-x^3 }{1-3x^2}$$
Hint:

Fill in the blanks

Question 1.
Principal value of sin-1 (-$$\frac {1}{2}$$) is ………………

Answer: –$$\frac {π}{6}$$

Question 2.
Principal value of sin-1 (-$$\frac {1}{√2}$$) is ……………….

Answer: $$\frac {-π}{4}$$

Question 3.
Principal value of cos-1 ($$\frac {-1}{2}$$) is ………………

Answer: $$\frac {2π}{3}$$

Question 4.
Principal value of tan-1 (-√3) is …………………

Answer: –$$\frac {π}{3}$$

Question 5.
Principal value of tan-1 (-1) is ……………..

Answer: –$$\frac {π}{4}$$

Question 6.
Principal value of cot-1 (√3) is ……………….

Answer: $$\frac {π}{6}$$

Question 7.
Principal value of cosec-1 (-√2) is ……………..

Answer: –$$\frac {π}{4}$$

Question 8.
sin-1 x + cos-1 x = ………………

Answer: $$\frac {π}{2}$$

Question 9.
tan-1 x + cot-1 x = ………………..

Answer: $$\frac {π}{2}$$

Question 10.
sec-1 x + cosec-1 x = ……………….

Answer: $$\frac {π}{2}$$

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