Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions
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:Answer/Explanation
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:Answer/Explanation
Explaination:
14. Find the principal value of tan-1√3 sec-1(-2). [NCERT; AI 2012] Answer:Answer/Explanation
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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 Answer:
(a) [3, 5] (b) [0, π] (c) [-√5 ,-√3] ∩ [-√5,√3] (d) [-√5 ,-√3] ∪ [√3, √5] Answer/Explanation
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:
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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:Answer/Explanation
Explaination:
29. Find the value of Answer:
[NCERT; Delhi 2013 (C), 2011] Answer/Explanation
Explaination:
30.
Answer/Explanation
Answer:
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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:
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33.
Answer/Explanation
Answer:
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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:Answer/Explanation
Explaination:
