Class 10 Maths Introduction to Trigonometry MCQ

1. 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

 

2. What is the maximum value of 1cscA?

A. 0
B. 1
C. 12
D. 2

ANSWER= B. 1

 

3. What is the minimum value of sin A, 0 ≤ A ≤ 90°

A. -1
B. 0
C. 1
D. 12

ANSWER= B. 0

 

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

A. -1
B. 0
C. 1
D. 12

ANSWER= B. 0

 

5. If cos 9A = sin A and 9A < 90°, then the value of tan 5A is

A. 0
B. 1
C. 13√
D. √3

ANSWER= B. 1

 

6. If in ΔABC, ∠C = 90°, then sin (A + B) =

A. 0
B. 1/2
C. 12√
D. 1

ANSWER= D. 1

 

7. If sin A – cos A = 0, then the value of sin4 A + cos4 A is

A. 2
B. 1
C. 34
D. 12

ANSWER= D. 12

 

8. Ratios of sides of a right triangle with respect to its acute angles are known as

A. trigonometric identities
B. trigonometry
C. trigonometric ratios of the angles
D. none of these

ANSWER= C. trigonometric ratios of the angles Explaination: C. trigonometric ratios of the angles

 

9. (sin A−2 sin3A)/ (2 cos3A−cos A)=

A. tan A
B. cot A
C. sec A
D. 1

ANSWER= A. tan A

 

10. In a right triangle ABC, the right angle is at B. Which of the following is true about the other two angles A and C?

A. There is no restriction on the measure of the angles
B. Both the angles should be obtuse
C. Both the angles should be acute
D. One of the angles is acute and the other is obtuse

ANSWER= C. Both the angles should be acute

 

11. (cos A / cot A) + sin A= ?

A. cot A
B. 2 sin A
C. 2 cos A
D. sec A

ANSWER= B. 2 sin A

 

12. If secθ + tanθ = x, then tanθ is:

A. (x2-1) / 2x
B. (x2+1) / 2x
C. (x2-1) / x
D. (x2+1) / x

ANSWER= A. (x2-1) / 2x

 

13. Which of the following numbers can form sides of a right angled triangle?

A. 13 cm , 27 cm , 15 cm
B. 4 cm , 5 cm , 9 cm
C. 2 cm , 17 cm , 9 cm
D. 10 cm , 6 cm , 8 cm

ANSWER= D. 10 cm , 6 cm , 8 cm

 

14. Which of the following are Pythagorean triplets?

A. 4 cm , 6 cm , 8 cm
B. 24 cm , 10 cm , 26 cm
C. 13 cm , 27 cm , 30 cm
D. 2 cm , 17 cm , 9 cm

ANSWER= B. 24 cm , 10 cm , 26 cm

 

15. If p cotθ = √(q2-p2), then the value of sinθ is- (θ being an acute angle)

A. q/3p
B. q/2p
C. p/q
D. 0

ANSWER= C. p/q

 

16. If sin A = 8/17, find the value of secA cosA + cosecA cosA.

A. 23/8
B. 15/8
C. 8/15
D. 6/23

ANSWER= A. 23/8

 

17. Which of the following is correct for some θ, such that 0° ≤θ< 90°

A. 1/ cos θ < 1
B. sec θ = 0
C. 1/ sec θ < 1
D. 1/ sec θ> 1

ANSWER= C. 1/ sec θ < 1

 

18. The value cot2 30°−2 cos2 60°−3/4 sec2 45°−4 sin2 30° is

A. 2
B. -1
C. 1
D. 0

ANSWER= D. 0

 

19. If 5tanθ=4, then value of (5sinθ -4cosθ)/(5sinθ +4cosθ) is:

A. 1/6
B. 5/6
C. 0
D. 5/3

ANSWER= C. 0

 

20. In △PQR, PQ = 12 cm and PR = 13 cm. ∠Q=90° Find tan P – cot R

A. –(119/60)
B. 119/60
C. 0
D. 1

ANSWER= C. 0

 

21. If tanθ= (x sinϕ) / (1−xcosϕ) and, tan ϕ = (y sin θ)/ (1−y cos θ) then x/y =

A. sinθ / (1−cosϕ)
B. sinθ / (1−cosθ)
C. sinθ/sinϕ
D. sinϕ / sinθ

ANSWER= C. sinθ/sinϕ

 

22. If Cosec (A+ B) = 2/√3, sec(A-B)=2/√3 0°

A. 25°,35°
B. 30°, 30°
C. 45°, 15°
D. 10°,50°

ANSWER= C. 45°, 15°

 

23. cos 1° × cos 2° × cos 3° ×……..× cos 180° is equal to:

A. 0
B. 1
C. ½
D. -1

ANSWER= A. 0

 

24. 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

 

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

A. 90°
B. 60°
C. 30°
D. 0°

ANSWER= D. 0°

 

26. If y sin 45° cos 45° = tan2 45° – cos2 30°, then y = …

A. –12
B. 12
C. -2
D. 2

ANSWER= B. 12

 

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

A. -1
B. 0
C. 1
D. 2

ANSWER= C. 1

 

28. 5 tan² A – 5 sec² A + 1 is equal to

A. 6
B. -5
C. 1
D. -4

ANSWER= D. -4

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