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^{-1}x = 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^{-1}x + cosec^{-1}y is

**Answer/Explanation**

Answer: b

Explaination:

19. The value of tan²(sec^{-1}2) + cot2(cosec^{-1}3) 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^{-1}3) = 7, state true or false.

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer: b

Explaination:

22.

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

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

⇒ x = √3

24. If sin^{-1}x + sin^{-1}y + sin^{-1}z = then the value of x + y² + z^{3} 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^{-1}x) = 1 then find the value of x. [NCERT; HOTS; Delhi 2014]

**Answer/Explanation**

Answer:

Explaination:

29. Find the value of

**Answer/Explanation**

Answer:

Explaination:

30.

**Answer/Explanation**

Answer:

Explaination:

31. Prove that 3 sin^{-1} x = sin^{-1}(3x – 4x^{3}),

**Answer/Explanation**

Answer:

Explaination:

Let x = sin θ

=> θ = sin^{-1}x

RHS = sin^{-1}(3x – 4x^{3})

= sin-^{-1} [3 sin θ – 4 sin^{3} θ] = sin^{-1} [sin 3θ] = 3θ = 3 sin^{-1}x = LHS

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

**Answer/Explanation**

Answer:

Explaination:

33.

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

Explaination: