The document consists of a series of trigonometry questions and answers, including various mathematical identities and equations. Each question presents a specific trigonometric problem, and multiple-choice options are provided for answers. The content appears to focus on reinforcing concepts in trigonometry for educational or examination purposes.

1. NDA:Maths:Trigonometry(pyqs)
1. sin3
   
3
1 cot cos 1 tan
       is equal to:
(a) sin – cos
  (b) sin cos
 
(c) sin cos
  (d) cosec sec
 

2. NDA:Maths :Trigonometry(pyqs)
2. The value of
6 6 2 2
sin cos 3sin cos
   is:
(a) 1 (b) 2
(c) 3 (d) 6

3. NDA:Maths :Trigonometry(pyqs)
3. If o o
0 x 90
  and 1 + tan2
x – 2tanx = 0, then the value of x is:
(a) 30o
(b) 45o
(c) 60o
(d) 90o

4. NDA:Maths :Trigonometry(pyqs)
4. The extremum values of cos x are:
(a)
– 3 1
and
2 2
(b) –1 and 0
(c) –1 and 1 (d) 0 and 1

5. NDA:Maths :Trigonometry(pyqs)
5. The value of sec can
(a) never be greater than 1
(b) never be less than 1
(c) never be equal to 1
(d) never lie between –1 and 1

6. NDA:Maths :Trigonometry(pyqs)
6. If x is acute, then
1 sin x
?
1– sin x


(a) sec x + tan x (b) cosec x + cot x
(c) sec x + cosec x (d) tan x + cot x

7. NDA:Maths :Trigonometry(pyqs)
7.
cos cos 1
?
1 sin 1– sin sec
 
 
 
 
   
 
(a) 4 (b) 2
(c) –2 (d) None

8. NDA:Maths :Trigonometry(pyqs)
8.    
cosec –sin sec –cos tan cot
      is equal to:
(a) 0 (b) 1
(c) –1 (d) None

9. NDA:Maths :Trigonometry(pyqs)
9.
3 3 3 3
sin cos cos – sin
?
sin cos cos – sin
 
   
 
 
   
 
(a) 2 (b) 1
(c) 0 (d) None

10. NDA:Maths :Trigonometry(pyqs)
10.
   
4 4
cos sin – cos – sin
?
sin cos
   

 
(a) 8 (b) 6
(c) 4 (d) None

11. NDA:Maths :Trigonometry(pyqs)
11. If x = r cos cos , y = r cos sin and z = rsin , then x2
+ y2
z2
= ?
(a) r2
(b) r4
(c) 1 (d) None

12. NDA:Maths :Trigonometry(pyqs)
12. The value of
2 2 2 2
2 2 2 2
sin cos cos sin
sin sin cos cos
   
    
is:
(a) 1 (b) 0
(c) –1 (d) 3

13. NDA:Maths :Trigonometry(pyqs)
13.
sin 1 cos
sin ?
1 cos sin
  
 
  
 
  
 
(a) 4 (b) 3
(c) 2 (d) 1

14. NDA:Maths :Trigonometry(pyqs)
14.  
sin cos –1
1 sin ?
sin – cos 1
 
 
  
 
 
 
(a) sin  (b) cos 
(c) tan  (d) None of these

15. NDA:Maths :Trigonometry(pyqs)
15.
2
sec tan –1
?
tan – sec 1
 
 

 
 
 
(a)
1– sin
1 sin

 
(b)
1 sin
1– sin
 

(c) 1 (d) None of these

16. NDA:Maths :Trigonometry(pyqs)
16.
2
cot – cosec 1
?
cot cosec –1
 
 

 
 
 
(a) cosec cot
  (b) cosec – cot
 
(c) 1 (d) None of these

17. NDA:Maths :Trigonometry(pyqs)
17. If sin cosec
   =2, then the value of  
2 2
sin cosec
   is:
(a) 1 (b) 2
(c) 4 (d) None

18. NDA:Maths :Trigonometry(pyqs)
18. If tan cot
  = 2, then the value of sin  is:
(a)
1
2
(b)
1
3
(c)
1
2
(d)
1
3

19. NDA:Maths :Trigonometry(pyqs)
19. (1 – sin A + cos A)2
= ?
(a) 2 (1 – sin A) (1 – cos A)
(b) 2 (1 + sin A) (1 – cos A)
(c) 2 (1 – sin A)(1 + cos A)
(d) None of these

20. NDA:Maths :Trigonometry(pyqs)
20. If
sin x sin x
4
1 cos x 1– cos x
 

and o o
0 x 90
  , then the value of x is:
(a) 10o
(b) 15o
(c) 30o
(d) 45o

21. NDA:Maths :Trigonometry(pyqs)
21. If  lies in second quadrant, then
1– sin 1 sin
– ?
1 sin 1– sin
  

  
(a) tan  (b) 2 tan 
(c) cot  (d) 2 cot 

22. NDA:Maths :Trigonometry(pyqs)
22. If
3
2

   
then
1 cos 1– cos
?
1– cos 1 cos
  
 
  
(a) 2 cosec  (b) –2 cosec 
(c) 2 sec  (d) –2 sec 

23. NDA:Maths :Trigonometry(pyqs)
23. If a tan  = b, the value of
bsin – a cos
bsin a cos
 
 
 
 
 
is:
(a)
2 2
2 2
b – a
b a

(b)
2 2
2 2
a – b
a b

(c)
2 2
2 2
a b
a – b

(d) None of these

24. NDA:Maths :Trigonometry(pyqs)
24. If 5 cot  = 4, then the value of
5sin – 3cos
is :
sin 2cos
 
 
 
 
 
is:
(a)
5
14
(b)
3
4
(c) 1 (d) None

25. NDA:Maths :Trigonometry(pyqs)
25. If sec – tan
  =,
2
3
then
(a)
5 2
sec ,tan
6 3
   
(b)
13 5
sec ,tan
12 12
   
(c)
8 4
sec ,tan
9 9
   
(d) None of these

26. NDA:Maths :Trigonometry(pyqs)
26. If cosec cot
  = 6, then :
(a)
35 37
cosec ,cot
12 12
   
(b)
37 35
cosec ,cot
12 12
   
(c)
41 31
cosec ,cot
12 12
   
(d) None of these

27. NDA:Maths :Trigonometry(pyqs)
27. If 2 2
7sin 3cos 4
   ,then the value of tan  is:
(a)
1
2
 (b)
1
3

(c)
1
2
 (d)
1
3


28. NDA:Maths :Trigonometry(pyqs)
28. If tan2
x = (1 – e2
), then the value of (sec x + tan3
x cosec x) is:
(a)  
3
2 2
2 e
 (b)  
3
2 2
2 – e
(c)  
3
2 2
1– e (d)  
3
2 2
1 e


29. NDA:Maths :Trigonometry(pyqs)
29. If 2
sin sin 1
   , then the value of 2 4
cos cos
  is:
(a) 0 (b) 1
(c) 2 (d) None

30. NDA:Maths :Trigonometry(pyqs)
30. If  
3sin 5cos 5
   , then the value of  
5sin – 3cos
  is:
(a) 4 (b) 3
(c) 2 (d) 1

31. NDA:Maths :Trigonometry(pyqs)
31. If    
1 sin 1 sin 1 sin
      =
   
1– sin 1– sin 1– sin
   = k, then k = ?
(a)  
cos cos cos
   
(b)  
sin sin sin
   
(c)  
3sin sin sin
   
(d) None of these

32. NDA:Maths :Trigonometry(pyqs)
32. If    
1 cos 1 cos 1 cos
      =
   
1– cos 1– cos 1– cos
   = k,then k = ?
(a)  
sin sin sin
   
(b)  
cos cos cos
   
(c)  
3cos cos cos
   
(d) None of these

33. NDA:Maths :Trigonometry(pyqs)
33. If
  
  
  
sec tan sec tan
sec – tan sec – tan
sec – tan sec – tan
    
 
 
   
 
 
   
 
= k, then the value of k is:
(a) 2
 (b) 3

(c) 1
 (d) 2


34. NDA:Maths :Trigonometry(pyqs)
34. If sec
4
– tan
3
   ,then the value of sin  is:
(a)
4
5
(b)
16
25
(c)
7
25
(d)
9
16

35. NDA:Maths :Trigonometry(pyqs)
35. If cosec – cot m
   , then the value of cos  is:
(a)
2
2
1 m
1– m

(b)
2
2
1– m
1 m

(c)
2
2
m –1
m 1

(d)
2
2
m 1
m –1


36. NDA:Maths :Trigonometry(pyqs)
36. If cos  + sin  = 2 cos  , then  
cos – sin
  = ?
(a) – 2 cos (b) 2 sin 
(c) 2cos (d) 2sin

37. NDA:Maths :Trigonometry(pyqs)
37. If acos bsin
  = 3 and
asin – bcos 4
   , then the value of (a2
+ b2
) is;
(a) 25 (b) 23
(c) 27 (d) None

38. NDA:Maths :Trigonometry(pyqs)
38. If acos – bsin c
   , then the value of  
a cos bcos
  is:
(a) 2 2 2
a b – c
  (b) 2 2 2
a – b c
 
(c) 2 2 2
a b c
   (d) 2 2 2
b c – a
 

39. NDA:Maths :Trigonometry(pyqs)
39. If cot cos mandcot – cos
     = n, then (m2
– n2
)2
is equal to:
(a) 4 mn (b) 8 mn
(c) 16 mn (d) None of these

40. NDA:Maths :Trigonometry(pyqs)
40. If tan sin mandtan –sin
    = n, then (m2
– n2
) = ?
(a) 4 mn (b) 4 mn
(c) 2 mn (d) 2 mn

41. NDA:Maths :Trigonometry(pyqs)
41. If 2 2 2
mcos nsin p, thencot ?
    
(a)
p n
p m


(b)
p – m
p – n
(c)
p – n
m – p
(d) None of these

42. NDA:Maths :Trigonometry(pyqs)
42. If 2
acos sin
  = p and 2
asin cos
  = q, then the value of
 
3
2 2
2 2
p q
p q

is:
(a) a (b) a2
(c) a3
(d) None

43. NDA:Maths :Trigonometry(pyqs)
43. If sin xcos andcos ysin ,
      , then the value of cos2
 is:
(a)
 
 
2
2 2
1 y
x – y

(b)
 
 
2
2 2
1– y
x – y
(c)
 
 
2
2 2
y –1
x – y
(d)
 
 
2 2
2 2
y x –1
x – y

44. NDA:Maths :Trigonometry(pyqs)
44. If a sec – btan 1
   and 2 2 2 2
a sec – b tan 5
   , then (4a2
– 9b2
) = ?
(a) a2
b2
(b) –a2
b2
(c) ab (d) –ab

45. NDA:Maths :Trigonometry(pyqs)
45. If asin bcos p
   and acos bsin q
   ,then (ap – bq)2
+ (aq – bq)2
= ?
(a) (a2
– b)2
(b) (a2
– b2
)2
(c) (a2
– b2
)3
(d) (a2
– b2
)4

46. NDA:Maths :Trigonometry(pyqs)
46. If 1 1 1
a cosec b cot c
  = 0
2 2 2
a cosec b cot c
  = 0, then
   
2 2
1 2 2 1 1 2 2 1
b c – b c – c a – c a = ?
(a)  
2
2 2 2 1
a b – a b (b)  
2
1 2 2 1
a b – a b
(c)  
2
1 1 2 2
a b – a b (d) None of these

47. NDA:Maths :Trigonometry(pyqs)
47. If x = a secn
 and y = b tann
 , then the  - eliminant is:
(a)
1 1
n n
x y
– 1
a b
   

   
   
(b)
2 2
n n
x y
– 1
a b
   

   
   
(c)
2 2
x y
– 1
a b
   

   
   
(d) None of these

48. NDA:Maths :Trigonometry(pyqs)
48. If x = cos3
 and y = b sin3
 , then  -eliminant is:
(a)
2
2
3
3
a b
1
x y
 
 
 
 
 
   
(b)
2
2
3
3
b a
1
x y
 
 
 
 
 
   
(c)
2 2
3 3
x y
1
a b
   
 
   
   
(d) None of these

49. NDA:Maths :Trigonometry(pyqs)
49. If x = a cos4
 ,and y = b sin4
 , then the  - eliminant is:
(a) x y 1
  (b)
x y
1
a b
 
(c)
1 1
4 4
x y
1
a b
   
 
   
   
(d) None of these

50. NDA:Maths :Trigonometry(pyqs)
50. If
x y
cos sin 1
a b
   and
,
x y
sin – cos 1
a b
   then the - eliminant is:
(a)
2 2
2 2
x y
0
a b
  (b)
2 2
2 2
x y
1
a b
 
(c)
2 2
2 2
x y
2
a b
  (d)
2 2
2 2
x y
–1
a b
 

51. NDA:Maths :Trigonometry(pyqs)
51. If x = h + p sec and y = k + q cosec , then
(a)
   
2 2
2 2
x – h y – k
1
p q
 
(b)
   
2 2
2 2
x – h y – k
– 1
p q

(c)
   
2 2
2 2
p q
– 1
x – h y – k

(d) None of these

52. NDA:Maths :Trigonometry(pyqs)