CPP- TRIGONOMETRIC RATIOS AND IDENTITIES - 2

FIITJ EE
EAST DELHI
CPP-VK
sin55  cos55
1. The value of is
sin10
1
(A) (B) 2 (C) 1 (D) 2
2

cot x  tan x
2. The value of is
cot 2x
(A) 1 (B) 2 (C) –1 (D) 4

b  ab ab
3. If tan   ,a  b  0 and if 0    , then  is equal to
a 4 ab ab
2 sin  2 cos  2 sin  2 cos 
(A) (B) (C) (D)
cos 2 cos 2 sin 2 sin 2

x x
4. If tan    cos ecx  sin x, then the value of tan2   IS
2
  2
(A) 2  5 (B) 2  5 (C) 2  5 (D) 2  5

5. If sin A  6 cos A  7 cos A, then cos A  6 sin A is equal to

(A) 6 sin A (B) – 7 sin A (C) 6 cos A (D) 7 cos A

6. If  and  satisfying 2 sec 2  = tan  + cot , then  +  is equal to

  
(A) (B) (C) (D) 
2 3 4

7. The value of sin 50° – sin 70° + sin 10° is

1 1
(A) 0 (B) 1 (C) (D)
2 2

8. sin 47° + sin 61° – sin 11° – sin 25° is equal to

(A) sin 7° (B) cos 7° (C) sin 36° (D) cos 36°

 2 4 8
9. The value of cos cos cos cos is
15 15 15 15
1 1
(A) (B) – (C) 1 (D) 0
16 16

2z tan 
10. If x sin   y cos   then 4z2(x2 + y2) is equal to
1  tan2 
(A) (x 2  y 2 )3 (B) (x 2  y 2 )3 (C) (x 2  y 2 )2 (D) (x 2  y 2 )2

11. The value of sin 36° sin 72° sin 108° sin 144° is
1 1 3 5
(A) (B) (C) (D)
4 16 4 16

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 
12. Let    0,  and t1  (tan )tan  , t 2  (tan )cot  , t3  (cot )tan  and t 4  (cot )cot  , then
 4
(A) t1  t 2  t 3  t 4 (B) t 4  t3  t1  t 2 (C) t 3  t1  t 2  t 4 (D) t 2  t 3  t1  t 4
 3 5 7
13. The value of sin sin sin sin is
16 16 16 16
2 1 1 2
(A) (B) (C) (D)
16 8 16 32

14. The value of sin 20°(4 + sec 20°) is

(A) 0 (B) 1 (C) 2 (D) 3

10 8 3 5
15. The expression cos  cos  cos  cos is equal to
13 13 13 13
(A) –1 (B) 0 (C) 1 (D) none of these

16. sin 12° sin 48° sin 54° is equal to

1 1 1 1
(A) (B) (C) (D)
16 32 8 4

17. The expression tan 9°– tan 27° – tan 63° + tan 81° is equal to
(A) 4 (B) 3 (C) 2 (D) 1

18. The value of the series cos 12° + cos 84° + cos 132° + cos 156° is
1 1 1 1
(A) (B) (C) – (D) –
2 4 4 2

   3   5   7 
19.  1  cos   1  cos   1  cos   1  cos  is equal to
 8  8  8  8 
1  1 1
(A) (B) cos (C) (D) –
2 8 8 2


20. If a  rad, then cos a + cos 2a + …+ cos 18a is equal to
18
(A) 0 (B) –1 (C) 1 (D) 1

n 1 A B
21. If sin A  n sinB, then tan is equal to
n1 2
A B A B A B
(A) sin (B) tan (C) cot (D) none of these
2 2 2
 
22. If sin 4A – cos 2A = cos 4A – sin2A,  0  A   , then the value of tan 4A is
 4
 3 
(A) 1 (B) (C) 3 (D)
3 3 1
21 27
23. Let ,  be such that       3 . If sin   sin    and cos   cos    , then the
65 65
(   )
value of cos is
2
3 3 6 6
(A)  (B) (C) (D) –
130 130 65 65
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24. The value of sin 10° + sin 20° + sin 30° + …+sin 360° is equal to
(A) 0 (B) 1 (C) 3 (D) 2

x x x sin x 1 x 1 x 1 x
25. If cos  cos 2  ....  cos n  , then tan  2 tan 2  ...  n tan n is
2 2 2 x 2 2 2 2 2 2
2n sin n
2
x 1  x 
(A) cot x  cot n (B) n cot  n   cot x
2 2 2 
1  x  1 1  x 
(C) n tan  n   tan x (D) cot x  n cot  n 
2 2  2 2 2 

1 t
26. Suppose 0 < t <  and sin t  cos t  . Then, tan is equal to
5 2
1
(A) 2 (B) 3 (C) (D) 5
3

27. tan  + 2 tan 2 + 4 tan 4 + 8 cot 8  is equal to

(A) tan 16  (B) 0 (C) cot  (D) none of these

28. The minimum value of 27cos2x .81sin2x is

1 1 1
(A) –5 (B) (C) (D)
5 243 27

29. The maximum value of 3 cos x + 4 sinx + 5 is

(A) 5 (B) 6 (C) 7 (D) none of these

2 sin x 1  sin x  cos x

30. If   , then equals
1  sin x  cos x 1  sin x

(A) 0 (B) – (C)  (D) 
2

31. If sin 6  32 cos5  sin   32 cos3  sin   3x, then x is equal to

(A) cos  (B) cos 2 (C) sin  (D) sin 2

 
32. The maximum value of 5 cos   3 cos      3 is
 3
(A) 5 (B) 11 (C) 10 (D) –1

33. If 5 cos x + 12 cos y = 13, then the maximum value of 5 sin x + 12 sin y is
(A) 12 (B) 120 (C) 20 (D) 13

34. The expression tan2 + cot2  is

(A)  2 (B) 2 (C)  –2 (D) none of these

A B
35. If A + B + C = 180°, then  tan 2 tan 2 is
(A) 0 (B) 1 (C) 2 (D) 3

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
36. The minimum value of f(x) = sin4x + cos4x, 0  x  is
2
1 1 1 1
(A) (B) (C) (D)
2 2 4 2 2

1
37. Minimum value of is
3 sin   4 cos   7
1 5 7 1
(A) (B) (C) (D)
12 12 12 6

 B  2C  3A   A B 
38. In a ABC, cos    cos   is equal to
 2   2 
(A) –1 (B) 0 (C) 1 (D) 2

39. If p  sin2 x  cos 4 x, then

3 3 1 1
(A)  p  1 (B) p (C) p 1 (D) none of these
4 16 4 4

A 1 B 2 C

40. Let A, B and C are the angles of a triangle and tan    , tan    . Then, tan   is
2
  3 2
  3 2
equal to

1 2 2 7
(A) (B) (C) (D)
3 3 9 9

41. If A + B + C = 270°, then cos 2A + cos 2B + cos 2C is equal to

(A) 4 sin A sin B sin C (B) 4 cos A cos B cos C
(C) 1 – 4 sin A sin B sin C (D) 1–4 cos A cos B cos C

ANSWERS
1. D 2. B 3. A 4. D
5. B 6. C 7. A 8. B
9. B 10. C 11. D 12. B
13. A 14. D 15. B 16. C
19. C 20. B 21. B 22. C
23. A 24. A 25. B 26. A
27. C 28. C 29. D 30. C
31. D 32. C 33. B 34. A
35. B 36. D 37. A 38. B
39. A 40. D 41. C

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