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Class 10 Maths Chapter 8 Introduction to Trigonometry

1. (sin30° + cos30°) – (sin 60° + cos60°)

(a) – 1

(b) 0

(c) 1

(d) 2

Answer: (b) 0

2. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is:

(a)12/7

(b)24/7

(c)20/7

(d)7/24

Answer: (b)24/7

3.  The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is

(a) 1

(b) -1

(c) 0

(d)√12

Answer: (c) 0

4. Given that sin α = 1/2 and cos β = 1/2, then the value of (α + β) is

(a) 0°

(b) 30°

(c) 60°

(d) 90°

Answer: (d) 90°

5.  If tanθ < 0, sinθ < 0, then the terminal arm of the angle lies in the quadrant

(a) 1

(b) 2

(c) 3

(d) 4

Answer: (a) 1

6. If x and y are complementary angles, then

(a) sin x = sin y

(b) tan x = tan y

(c) cos x = cos y

(d) sec x = cosec y

Answer: (d) sec x = cosec y

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7. Value of tan30°/cot60° is:

(a) 1/√2

(b) 1/√3

(c) √3

(d) 1

Answer: (d) 1

8.  (Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:

(a)0

(b)1+2√3

(c)1-√3

(d)1+√3

Answer: (c)1-√3

9.  If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to

(a) √3

(b) 12

(c) √12

(d) 1

Answer: (d) 1

10. sin (45° + θ) – cos (45° – θ) is equal to

(a) 2 cos θ

(b) 0

(c) 2 sin θ

(d) 1

Answer: (b) 0

11.  In right triangle ABC, right angled at C, if tan A = 1, then the value of 2 sin A cos A is

(a) 0

(b) 1

(c) – 1

(d) 2

Answer: (b) 1

12.  sin 2B = 2 sin B is true when B is equal to

(a) 90°

(b) 60°

(c) 30°

(d) 0°

Answer: (d) 0°

13.  sec2θ – 1 = ?

(a) tan2θ

(b) tan2θ + 1

(c) cot2θ – 1

(d) cos2θ

Answer:  (a) tan2θ

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14. The value of tan 60°/cot 30° is equal to:

(a)0

(b)1

(c)2

(d)3

Answer: (b)1

15.  If x and y are complementary angles, then

(a) sin x = sin y

(b) tan x = tan y

(c) cos x = cos y

(d) sec x = cosec y

Answer: (d) sec x = cosec y

16. If √2 sin (60° – α) = 1 then α is

(a) 45°

(b) 15°

(c) 60°

(d) 30°

Answer: (b) 15°

17.  If cos (α + β) = 0, then sin (α – β) can be reduced to

(a) cos β

(b) cos 2β

(c) sin α

(d) sin 2α

Answer: (b) cos 2β

18.  If ΔABC is right angled at C, then the value of cos (A + B) is

(a) 0

(b) 1

(c) 1/2

(d) √3/2

Answer: (a) 0

19. The value of sin θ and cos (90° – θ)

(a) Are same

(b) Are different

(c) No relation

(d) Information insufficient

Answer: (a) Are same

20. 1-cos²A is equal to:

(a)sin²A

(b)tan²A

(c)1-sin²A

(d)sec²A

Answer: (a)sin2A

21. sin 2B = 2 sin B is true when B is equal to

(a) 90°

(b) 60°

(c) 30°

(d) 0°

Answer: (d) 0°

22. The value of sin² 30° – cos² 30° is

(a) –1/2

(b) √3/2

(c) 3/2

(d) –2/3

Answer: (a) –1/2

23. Given that sin A=1/2 and cos B=1/√2 then the value of (A + B) is:

(a) 30°

(b) 45°

(c) 75°

(d) 15°

Answer: (c) 75°

24. If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ____

(a) -1

(b) 0

(c) 1

(d) 2

Answer: (c) 1

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25.  If cos A = 4/5, then tan A = ?

(a) 3/5

(b) 3/4

(c) 4/3

(d) 4/5

Answer: (b) ¾

26. If cos X = ⅔ then tan X is equal to:

(a)5/2

(b)√(5/2)

(c)√5/2

(d)2/√5

Answer: (c)√5/2

27.  If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to

(a) 0

(b) √13

(c) 1

(d) √3

Answer: (c) 1

28. If cos (40° + A) = sin 30°, then value of A is

(a) 30°

(b) 40°

(c) 60°

(d) 20°

Answer: (d) 20°

29. The value of θ for which 2 cos2θ + sinθ – 2 =; 0° < θ < 90° is:​

(a) 60°

(b) 10°

(c) 30°

(d) 45°

Answer: (c) 30°

30.  If x = a cos 0 and y = b sin 0, then b²x² + a²y² =

(a) ab

(b) b² + a²

(c) a²b²

(d) a⁴b⁴

Answer: (c) a²b²

31.  The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is

(a) 1

(b) −1

(c) 0

(d) 1/2

Answer: (c) 0

32.  If cos X=a/b, then sin X is equal to:

(a)b2-a2/b

(b)b-a/b

(c)√(b2-a2)/b

(d)√(b-a)/b

Answer: (c)√(b2-a2)/b

33. 5 tan² A – 5 sec² A + 1 is equal to

(a) 6

(b) -5

(c) 1

(d) -4

Answer: (d) -4

34. If cosec θ – cot θ = 13, the value of (cosec θ + cot θ) is

(a) 1

(b) 2

(c) 3

(d) 4

Answer: (c) 3

35. 7 sin² θ + 3 cos² θ = 4 then :

(a) tan θ = 1/√2

(b) tan θ = 1/2

(c) tan θ = 1/3

(d) tan θ = 1/√3

Answer: (d) tan θ = 1/√3

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36.  If cos A + cos² A = 1, then sin² A + sin⁴ A is

(a) -1

(b) 0

(c) 1

(d) 2

Answer: (c) 1

37. The value of (tan1° tan2° tan3° … tan89°) is

(a) 0

(b) 1

(c) 2

(d)1/2

Answer: (b) 1

38. 2tan 30°/1+tan230° =

(a)Sin 60°

(b)Cos 60°

(c)Tan 60°

(d)Sin 30°

Answer: (a)Sin 60°

39. What is the minimum value of cos θ, 0 ≤ θ ≤ 90°

(a) -1

(b) 0

(c) 1

(d) 1/2

Answer: b

40. 1+tan²A1+cot²A  is equal to

(a) sec² A

(b) -1

(c) cot² A

(d) tan² A

Answer: (d) tan² A

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