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

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) –$$\frac{\pi}{4}$$

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

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

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.

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

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

Explaination: 10. Find the principal value of cos-1 $$\frac{1}{2}$$.

Explaination: 11. Find the principal value of Explaination: 12. What is the domain of the function sin-1 x?

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]

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

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

Explaination: 16. If tan-1 x -cot-1 = $$\frac{\pi}{6}$$, then x is ______ .

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

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

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.

Explaination: 21. If 3 sin-1x + cos-1x = π, then x is equal to Explaination: 22. Explaination: 23. If cos(tan-1x + cot-1√3) = 0, then value of x is _____ .

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

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]

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

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

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

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

Explaination: 30. Explaination:  31. Prove that 3 sin-1 x = sin-1(3x – 4x3), 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$$\left(\frac{x}{\sqrt{1-x^{2}}}\right)$$

Explaination: 33. Explaination: 34. If sin-1x + sin-1y = $$\frac{2 \pi}{3}$$, then find the value of cos-1x + cos-1y.

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