trigonomentry

Question 1

1. 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 1

c)0

Question 2

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

(a) √3
(b) 12
(c) 12√
(d) 1

Answer 2

d)1

Question 3

3. 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 3

(d) sec x = cosec y

Question 4

4. sin 2B = 2 sin B is true when B is equal to
   (a) 90°
   (b) 60°
   (c) 30°
   (d) 0°

Answer 4

(d) 0°

Question 5

5. If A, B and C are interior angles of a ΔABC then cos(B+C2) is equal to
   a) sin A/2
   b) -sin A/2
   c) cos A/2
   d) -cos A/2

Answer 5

a) sin A/2

Question 6

6. 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 6

c)1

Question 7

7. If y sin 45° cos 45° = tan2 45° – cos2 30°, then y = …
   (a) –1/2
   (b) 1/2
   (c) -2
   (d) 2

Answer 7

b)1/2

Question 8

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

(a) -1
(b) 0
(c) 1
(d) 2

Answer 8

c)1

Question 9

9. 5 tan² A – 5 sec² A + 1 is equal to
   (a) 6
   (6) -5
   (c) 1
   (d) -4

Answer 9

d)-4

Question 10

10. If sec A + tan A = x, then sec A =

Answer 10

x^2+1/2x

Question 11

11. If sec A + tan A = x, then tan A =

Answer 11

x^2-1 /2x

Question 12

13. If x = a cos 0 and y = b sin 0, then b2x2 + a2y2 =
    (a) ab
    (b) b² + a²
    (c) a²b²
    (d) a4b4

Answer 12

(c) a²b²

Question 13

14. What is the maximum value of 1/csc A?
    (a) 0
    (b) 1
    (c) 12
    (d) 2

Answer 13

b)1

Question 14

15. What is the minimum value of sin A, 0 ≤ A ≤ 90°
    (a) -1
    (b) 0
    (c) 1
    (d) 12

Answer 14

(b) 0

Question 15

16. What is the minimum value of cos θ, 0 ≤ θ ≤ 90°
    (a) -1
    (b) 0
    (c) 1
    (d) 12

Answer 15

(b) 0

Question 16

17. Given that sin θ = ab , then tan θ =

Answer 16

a/ root b^2-a^2

Question 17

18. If cos 9A = sin A and 9A < 90°, then the value of tan 5A is
    (a) 0
    (b) 1
    (c) 13√
    (d) √3

Answer 17

b)1

Question 18

19. If in ΔABC, ∠C = 90°, then sin (A + B) =
    (a) 0
    (b) 1/2
    (c) 12√
    (d) 1

Answer 18

d)1

Question 19

20. If sin A – cos A = 0, then the value of sin4 A + cos4 A is
    (a) 2
    (b) 1
    (c) 3/4
    (d) 1/2

Answer 19

d)1/2

Question 20

21. 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 20

(b)24/7

AB=24cm and BC = 7cm

Tan C = Opposite side/Adjacent side

Tan C=24/7

Question 21

22. (Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:
    (a) 0
    (b) 1+2√3
    (c) 1-√3
    (d) 1+√3

Answer 21

(c)1-√3

sin 30° = ½, sin 60° = √3/2, cos 30° = √3/2 and cos 60° = ½

Putting these values, we get:

(½+½)-(√3/2+√3/2)

= 1-√3

Question 22

23. The value of tan 60°/cot 30° is equal to:
    (a) 0
    (b) 1
    (c) 2
    (d) 3

Answer 22

(b)1

Explanation: tan 60° = √3 and cot 30° = √3

Hence, tan 60°/cot 30° = √3/√3 = 1

Question 23

24. 1-cos2A is equal to:
    (a) sin2A
    (b) tan2A
    (c) 1-sin2A
    (d) sec2A

Answer 23

(a)sin2A

We know, by trigonometry identities,
sin2A+cos2A = 1
1-cos2A = sin2A

Question 24

25. . Sin (90° – A) and cos A are:
    (a) Different
    (b) Same
    (c) Not related
    (d) None of the above

Answer 24

(b)Same

By trigonometry identities.
Sin (90°-A) = cos A [comes in the first quadrant of unit circle]

Question 25

26. If cos X = ⅔ then tan X is equal to:
    (a) 5/2
    (b) √(5/2)
    (c) √5/2
    (d) 2/√5

Answer 25

(c)√5/2

 By trigonometry identities, we know:
1+tan2X=sec2X
And sec X = 1/cos X = 1/(⅔) = 3/2
Hence,
1+tan2X=(3/2)2=9/4
tan2X=9/4-1=5/4
Tan X = √5/2

Question 26

27. 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 26

(c)√(b2-a2)/b

 cos X=a/b
By trigonometry identities, we know that:
sin2X+cos2X=1
sin2X=1-cos2X = 1-(a/b)2
Sin X=√(b2-a2)/b

Question 27

28.The value of sin 60° cos 30° + sin 30° cos 60° is:

(a) 0
(b) 1
(c) 2
(d) 4

Answer 27

(b)1

sin 60° = √3/2, sin 30° = ½, cos 60° = ½ and cos 30° = √3/2
Therefore,
√3/2 x √3/2 + ½ x ½
= 3/4 + 1/4
= 1

Question 28

29. 2tan 30°/1+tan230° =

(a) Sin 60°
(b) Cos 60°
(c) Tan 60°
(d) Sin 30°

Answer 28

(a)Sin 60°

tan 30° = 1/√3
Putting this value we get;
2(1/√3)/1+(1/√3)2 = (2/√3)/4/3 = 6/4√3 = √3/2 = sin 60°

Question 29

30.sin 2A = 2 sin A is true when A =

(a) 30°
(b) 45°
(c) 0°
(d) 60°

Answer 29

(c)0°

sin 2A = sin 0° = 0
2sin A = 2sin 0° = 0