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

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

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

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

Answer

Answer: (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

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

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) \(\frac { 1 }{2}\)

Answer

Answer: (c) 0


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

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

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

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

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

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

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.

Answer

Answer: (d) 4 sin² α.
Hint:
MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers 1
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

Answer

Answer: (a) 3
Hint:
MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers 2


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

Answer: (b) \(\frac { 6 }{17}\)
Hint:
MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers 3


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

Answer: (a) \(\frac { 3x-x^3 }{1-3x^2}\)
Hint:
MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers 4


Fill in the blanks

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

Answer

Answer: –\(\frac {π}{6}\)


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

Answer

Answer: \(\frac {-π}{4}\)


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

Answer

Answer: \(\frac {2π}{3}\)


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

Answer

Answer: –\(\frac {π}{3}\)


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

Answer

Answer: –\(\frac {π}{4}\)


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

Answer

Answer: \(\frac {π}{6}\)


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

Answer

Answer: –\(\frac {π}{4}\)


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

Answer

Answer: \(\frac {π}{2}\)


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

Answer

Answer: \(\frac {π}{2}\)


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

Answer

Answer: \(\frac {π}{2}\)


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