Mathematics Inverse Trigonometric Functions Online Test

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You can prepare for Mathematics Inverse Trigonometric Functions Online Test by attempting the free online quizzes at Gotest.com.pk. We provide instant results, performance reports, and detailed explanations for every question.

Question 1

1. Tan⁻¹ (2A/1 – A²) =

Answer

Tan⁻¹ A

Answer

2 Tan⁻¹ A

Answer

Tan⁻¹(A/2) =

Answer

Tan⁻¹(2/A) =

Question 2

2. The values of θ satisfying sin 7 θ = sin 4 θ – sin θ and 0 < θ < π/2 are

Answer

π/6, π/9

Answer

π/9, π/4

Answer

π/3, π/4

Answer

π/3, π/9

Question 3

3. The number of values of x in the interval [0, 5π] satisfying the equation 3 sin² x – 7 sinx + 2 = 0 is

Question 4

4. The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is

Answer

(-1)ⁿ nπ/2 + π/8

Answer

2nπ + cos⁻¹ (3/4)

Answer

nπ + π/8

Answer

nπ/2 + π/8

Question 5

5. If 4 sin² θ = 1, then values of θ are

Answer

2nπ ± π/3

Answer

nπ ± π/3

Answer

nπ ± π/6

Answer

2nπ ± π/6

Question 6

6. If sin 6 θ + sin 4 θ + sin 2 θ = 0, then θ =

Answer

nπ/4 or 2nπ ± π/6

Answer

nπ/4 or nπ ± π/3

Answer

nπ/4 or nπ ± π/6

Answer

None of these

Question 7

7. The domain of principal cosine function is

Answer

[0, 3π/2]

Question 8

8. The principal cosine function is

Answer

One – to – one

Question 9

9. Sin⁻¹{2A√1 – A²}

Answer

Sin⁻¹{A² – 2}

Answer

Sin⁻¹{2A² – 1}

Answer

Sin⁻¹{A² – 2}

Answer

Sin⁻¹{2A² – 1}

Question 10

10. The general solution of tan 3x = 1 is

Answer

nπ + π/4

Answer

nπ/3 + π/12

Answer

nπ ± π/4

Question 11

11. If (1 + tan θ)(1 + tan Ø) = 2, then θ + Ø =

Question 12

12. One root of the equation cos x – x + ½ = 0 lies in the interval

Answer

(π, 3π/2)

Answer

(π/2, π)

Answer

(– π/2, 0)

Question 13

13. Range of Tan⁻¹ x is

Answer

[– π/2, π/2]

Answer

[π/2, π/2]

Question 14

14. The set of values of x for which tan3x–tan2x/1+tan3xtan2x = 1 is

Answer

2nπ + π/4 n = 1,2,3,……

Answer

nπ + π/4 n = 1,2,3,……

Question 15

15. Which of the following is solution of cos 3x = ½ = ?

Answer

1/3 arc cos ½

Answer

Arc cos 1/6

Question 16

16. Tan⁻¹ A – Tan⁻¹ B =

Answer

Tan⁻¹(A + B/1 – AB)

Answer

Tan⁻¹(1+AB/A – B)

Answer

Tan⁻¹(A – B/1+AB)

Answer

Tan⁻¹(1–AB/A+B)

Question 17

17. The number of solutions of the equation tan x + sec x = 2 cos lying the interval [0, 2π] is

Question 18

18. Tan⁻¹ 1/3 + Tan⁻¹ 1/5 + Tan⁻¹ 1/7 + Tan⁻¹ 1/8

Question 19

19.

Question 20

20.

Question 21

21. Tan⁻¹(1) =

Answer

None of these

Question 22

22. The domain of the function y = cos⁻¹ x is

Answer

– 1 ≤ x ≤ 1

Answer

0 ≤ x ≤ 1

Answer

– 1 ≤ x ≤ 2

Answer

– 2 ≤ x ≤ 2

Question 23

23. The solution set of the system of equation: x – y = 2π/3, cos x + cos y = 2/3, where x and y are real in:

Answer

None of these

Answer

a fine non-empty set

Question 24

24. For n ϵ Z, the general solution of the equation (√3 – 1)sin θ + (√3 + 1) cos θ = 2 is

Answer

θ = 2nπ ± π/4 + π/12

Answer

θ = nπ +(-1)ⁿ π/4 + π/12

Answer

None of these

Answer

θ = 2nπ ± π/4 - π/12

Question 25

25. tan⁻¹(1/4) + tan⁻¹(2/9) is equal to

Answer

½ cos⁻¹ (3/5)

Answer

tan⁻¹ ½

Answer

½ sin⁻¹ (3/5)

Answer

½ tan⁻¹ (3/5)

Question 26

26. If sin A = sin B, cos A = cos B, then the value of A in terms of B is

Answer

2nπ – B

Answer

nπ + (– 1)ⁿ B

Question 27

27. Range of cosec⁻¹x is

Answer

None of these

Answer

[– π/2, π/2]

Question 28

28. Tan⁻¹ ½ + Tan⁻¹ 1/13 =

Question 29

29.

Question 30

30. Tan⁻¹ A + Tan⁻¹ (1–A/1+A)

Question 31

31.

Question 32

32. Tan⁻¹ 1/7 + Tan⁻¹ 1/13 =

Answer

Tan⁻¹ 3/46

Answer

Tan⁻¹ 2/9

Answer

Tan⁻¹ 2/9

Answer

Tan⁻¹ 9/2

Question 33

33. Tan⁻¹(– 1) =

Question 34

34. If 5 cos 2 θ + 2 cos² θ/2 + 1 = 0, - π < θ < π, then θ =

Answer

cos – 1 3/5

Answer

π/3, cos⁻¹ (3/5)

Answer

± π/3, π – cos⁻¹ 3/5

Question 35

35. The smallest positive root of the equation tan x – x = 0 lies on

Answer

(π/2, π)

Answer

(π, 3π/2)

Answer

(3π/2, 2π)

Question 36

36. The principal tangent function is

Answer

None of these

Answer

One – to – one

Question 37

37. The value of cos [cos⁻¹ (- √3/2) + π/6] is

Answer

None of these

Question 38

38.

Question 39

39. The solution of the equation cos² θ + sin θ + 1 = 0 lies in the interval

Answer

(- π/4, π/4)

Answer

(3π/4, 5π/4)

Answer

(5π/4, 7π/4)

Answer

(π/4, 3π/4)

Question 40

40. cot θ = sin 2 θ (θ ≠ nπ, n integer) if θ =

Answer

π/4, π/3

Answer

π/4, π/2

Question 41

41. If sin⁻¹ x = π/5 for some x ϵ (-1,1), then the value of cos⁻¹x is

Question 42

42. The domain of principal sine function is

Answer

[0, 3π/2]

Answer

[–π/2, π/2]

Question 43

43. The value of sin [arc cos (- ½ )]is

Answer

None of these

Question 44

44. 2Cos⁻¹ A =

Answer

Sin⁻¹{2A² – 1}

Answer

Sin⁻¹{A² – 2}

Answer

Sin⁻¹{A² – 2}

Answer

Sin⁻¹{2A² – 1}

Question 45

45. General solution of tan 5 θ = cot 2 θ is

Answer

θ = nπ/7 + π/14 where n ϵ Z

Answer

θ = nπ/7 + π/2

Answer

θ = nπ/7 + π/3

Answer

nπ/7 + π/14

Question 46

46. The equation 2 cos²(x/2) sin²x = x² + 1/x² 0 ≤ x ≤ π/2 has

Answer

One real solution

Answer

None of these

Answer

Total Questions:	55
Time Allowed:	20 Minutes
Total Marks:	55
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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