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Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Inverse Trigonometric Functions MCQs Pdf with Answers to know their preparation level.

Inverse Trigonometric Functions Class 12 Maths MCQs Pdf

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

Answer/Explanation

Answer: d
Explaination:


2. sin-1{sin (\(\frac{2 \pi}{3}\))} = \(\frac{2 \pi}{3}\), state true or false.

Answer/Explanation

Answer:
Explaination: False, as –\(\frac{\pi}{2}\) ≤ sin<sup>-1</sup> x ≤ \(\frac{\pi}{2}\).


3. tan-1{sin (-\(\frac{\pi}{2}\))} is equal to
(a) -1
(b) 1
(c) \(\frac{\pi}{2}\)
(d) –\(\frac{\pi}{4}\)

Answer/Explanation

Answer: d
Explaination:
(d), as sin (-\(\frac{\pi}{2}\))= -1, and tan<sup>-1</sup>(-1) = – \(\frac{\pi}{4}\).


4. sec{tan-1 (-\(\frac{y}{3}\))} is equal to

Answer/Explanation

Answer: b
Explaination:


5. Principal branch of tan-1 x is ______ .

Answer/Explanation

Answer:
Explaination:


6. Principal value of the expression cos-1[cos(-680°)] is

Answer/Explanation

Answer: a
Explaination:
(a), as cos(-680°) = cos 680°
= cos(720° – 40°) = cos 40°
∴ cos<sup>-1</sup>[cos(-680°)J = cos<sup>-1</sup> (cos 40°)
= 40° = \(\frac{2 \pi}{9}\).


7. If tan-1x = sin-1(\(\frac{1}{\sqrt{2}}\)),then x is ______ .

Answer/Explanation

Answer:
Explaination: 1, as tan<sup>-1</sup> x = \(\frac{\pi}{4}\).


8. cos-1 \(\left(\cos \frac{7 \pi}{6}\right)=\frac{7 \pi}{6}\), state true or false.

Answer/Explanation

Answer:
Explaination: False, as \(\frac{7 \pi}{6}\) ∉ [0, π].


9. Find the value of tan-1 √3 – cot-1(-√3). [CBSE 2018]

Answer/Explanation

Answer:
Explaination:


10. Find the principal value of cos-1 \(\frac{1}{2}\).

Answer/Explanation

Answer:
Explaination:


11. Find the principal value of

Answer/Explanation

Answer:
Explaination:


12. What is the domain of the function sin-1 x?

Answer/Explanation

Answer:
Explaination: -1 ≤ x ≤ 1 or [-1, 1]


13. Find the value of sin\(\left[\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right]\). [NCERT; Delhi 2011]

Answer/Explanation

Answer:
Explaination:


14. Find the principal value of tan-1√3 sec-1(-2). [NCERT; AI 2012]

Answer/Explanation

Answer:
Explaination:


15. If sin-1 x = \(\frac{\pi}{10}\), for some x ∈ R, then the value of cos-1 is ______ .

Answer/Explanation

Answer:
Explaination:


16. If tan-1 x -cot-1 = \(\frac{\pi}{6}\), then x is ______ .

Answer/Explanation

Answer:
Explaination:


17. The domain of the function^ = sin’ -‘(V) is
(a) [0, 1]
(b) (0, 1)
(c) [-1, 1]
(d) Φ

Answer/Explanation

Answer: c
Explaination:
(c), as -1 ≤ -x² < 1
⇒ 1 ≥ x² ≥ -1
⇒ 0 ≤ x² ≤ 1
⇒ |x| ≤ 1
⇒ -1 ≤ x ≤ 1.


18. If sec-1 x + sec-1 y = \(\frac{\pi}{2}\) the value of cosec-1x + cosec-1y is

Answer/Explanation

Answer: b
Explaination:


19. The value of tan²(sec-12) + cot2(cosec-13) is
(a) 5
(b) 11
(c) 13
(d) 15

Answer/Explanation

Answer: b
Explaination:
(b), as tan²(sec<sup>-1</sup>2) + cot²cosec<sup>-1</sup>3)
= sec²(sec<sup>-1</sup>2) – 1 + cosec²(cos 3) – 1
= (2)² – 1 +(3)² – 1
= 4 – 1 +9 – 1 = 11.


20. cot(\(\frac{\pi}{4}\) – 2 cot-13) = 7, state true or false.

Answer/Explanation

Answer:
Explaination:


21. If 3 sin-1x + cos-1x = π, then x is equal to

Answer/Explanation

Answer: b
Explaination:


22.

Answer/Explanation

Answer:
Explaination:


23. If cos(tan-1x + cot-1√3) = 0, then value of x is _____ .

Answer/Explanation

Answer:
Explaination: √3, as tan-1x + cot-1 √3 = \(\frac{\pi}{2}\)
⇒ x = √3


24. If sin-1x + sin-1y + sin-1z = then the value of x + y² + z3 is
(a) 1
(b) 3
(c) 2
(d) 5

Answer/Explanation

Answer: b
Explaination:


25. The domain of y = cos-1(x² – 4) is
(a) [3, 5]
(b) [0, π]
(c) [-√5 ,-√3] ∩ [-√5,√3]
(d) [-√5 ,-√3] ∪ [√3, √5]

Answer/Explanation

Answer:
Explaination:


26. Show that sin-1(2x\(\sqrt{1-x^{2}}\)) = 2 sin-1 – \(\frac{1}{\sqrt{2}}\) ≤ x ≤ \(\frac{1}{\sqrt{2}}\)

Answer/Explanation

Answer:
Explaination:


27. Find the value of sec(tan-1 –\(\frac{1}{2}\)).

Answer/Explanation

Answer:
Explaination:


28. If sin(sin-1\(\frac{1}{5}\) + cos-1x) = 1 then find the value of x. [NCERT; HOTS; Delhi 2014]

Answer/Explanation

Answer:
Explaination:


29. Find the value of
[NCERT; Delhi 2013 (C), 2011]

Answer/Explanation

Answer:
Explaination:


30.

Answer/Explanation

Answer:
Explaination:


31. Prove that 3 sin-1 x = sin-1(3x – 4x3),

Answer/Explanation

Answer:
Explaination:
Let x = sin θ
=> θ = sin-1x
RHS = sin-1(3x – 4x3)
= sin--1 [3 sin θ – 4 sin3 θ]
= sin-1 [sin 3θ] = 3θ = 3 sin-1x = LHS


32. Prove that sin-1x = tan-1\(\left(\frac{x}{\sqrt{1-x^{2}}}\right)\)

Answer/Explanation

Answer:
Explaination:


33.

Answer/Explanation

Answer:
Explaination:


34. If sin-1x + sin-1y = \(\frac{2 \pi}{3}\), then find the value of cos-1x + cos-1y.

Answer/Explanation

Answer:
Explaination:


35. Find the value oftan(2 tan-1 \(\frac{1}{5}\)). [Delhi 2013]

Answer/Explanation

Answer:
Explaination:


We hope the given Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions will help you. If you have any query regarding CBSE Class 12 Maths Inverse Trigonometric Functions MCQs Pdf, drop a comment below and we will get back to you at the earliest.

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