These Inverse Trigonometric Functions Class 12 Questions And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Inverse Trigonometric Functions Class 12 Questions And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Inverse Trigonometric Functions Class 12 Questions And Answers

1. The value of cos^{-1}(1/2) + 2sin^{-1}(1/2) is equal to

(A) π/4

(B) π/6

(C) 2π/3

(D) 5π/6

**Answer:** π/6

2. tan^{-1}1/2 + tan^{-1}1/3 =

(A) π/4

(B) π/2

(C) π/3

(D) π

**Answer:** π/4

3. Which of the following is the principal value branch of cosec^{-1} x?

(A) (−π/2, π/2)

(B) (0, π) – {π/2}

(C) [−π/2, π/2]

(D) [−π/2, π/2] – [0]

**Answer:** [−π/2, π/2] – [0]

4. The principle value of sin-1(sin2π/3)is

(A) 2π/3

(B) π/3

(C) -π/6

(D) π/6

**Answer:** π/3

5. cos^{-1}(cos7π/6) is equal to

(A) 7π/6

(B) 5π/6

(C) π/3

(D) π/6

**Answer:** 5π/6

6. cosec^{-1}(2)

(A) π/6

(B) 2π/3

(C) 5π/6

(D) 0

**Answer:** π/6

7. If 6 sin^{-1} (x² – 6x + 8.5) = π, then x is equal to

(A) 1

(B) 2

(C) 3

(D) 8

**Answer:** 2

8. tan^{-1} √3 – sec^{-1}(-2)

(A) π

(B) –π/3, 0

(C) π/3

(D) 2π/3

**Answer:** –π/3, 0

9. sin(sec^{-1} x + cosec^{-1}x) =

(A) 1

(B) -1

(C) π/2

(D) π/3

**Answer:** 1

10. sin^{-1} (1 – x) – 2 sin^{-1} x = π/2 then x = ?

(A) 0, 1/2

(B) 1, 1/2

(C) 1/2

(D) 0

**Answer:** 0

11. The value of x for which sin |cot^{-1}(1 – x)| = cos (tan^{-1} x) is

(A) 2/1

(B) 1

(C) 0

(D) 1/2

**Answer:** 1/2

12. 4 tan^{-1} 15 – tan^{-1} 1/239

(A) π

(B) π/2

(C) π/3

(D) π/4

**Answer:** π/4

13. Principal value of sin^{-1}(1√2)

(A) π/4

(B) 3π/4

(C) 5π/4

(D) None of these

**Answer:** π/4

14. The principal value of cosec^{-1} (-2) is

(A) –2π/3

(B) π/6

(C) 2π/3

(D) –π/6

**Answer:** –π/6

15. Which of the following is the principal value branch of cos^{-1} x?

(A) [−π/2, π/2]

(B) (0, π)

(C) (0, π)

(D) (0, π) – {π/2}

**Answer:** (0, π)

16. If 3 tan^{-1} x + cot^{-1} x = π, then x equals

(A) 0

(B) 1

(C) -1

(D) 1/2

**Answer:** 1

17. The domain of the function cos^{-1} (2x – 1) is

(A) [0, 1]

(B) [-1, 1]

(C) [-1, -1]

(D) [0, π]

**Answer:** [0, 1]

18. If tan^{-1} x + tan^{-1} y = 4π5 then cot^{-1} x + cot^{-1} y equals

(A) π/5

(B) 2π/5

(C) 3π/5

(D) π

**Answer:** π/5

19. If cos^{-1} α + cos^{-1} β + cos^{-1} γ = 3π, then α(β + γ) + β (γ + α) + γ(α + β) equals

(A) 0

(B) 1

(C) 6

(D) 12

**Answer:** 6

20. If cos^{-1} x > sin^{-1} x, then

(A) 1/√2 < x ≤ 1

(B) 0 ≤ x < 1/√2

(C) -1 ≤ x < 1/√2

(D) x > 0

**Answer:** 0 ≤ x < 1/√2