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Mohanty Classes
Mob-9971649020 , B-1,Vasant Kunj,ND-70, www.mohantyclasses.com
2 6

,  
5

3
9


18. If sin A  and cos B  , 0  A  , 0  B  ,find the values of the following (i)
5
41
2
2
17. Find all other trigonometric ratios if, sin  
sin  A  B  (ii) sin  A  B  (iii) cos  A  B 
1
3
and    
find the value of 4 tan 2   3cos ec 2 
2
2
rd
nd
20. If cot x =1/2,secy =- 5/3,find the value of tan(x+y), x in 3 and y in 2 qudrant
19. If cos   
21. If cot x 
5
1
, sec y   ,find the value of
2
3
tan  x  y  , x is in 3 rd and y in 2 nd
quadrant.
3
12
22. If sin x  , cos y   , where x and y both lie in II quadrant, find the value of sin  x  y  .
5
13
5
23. If cot x   , x lies in II quadrant, find the value of sec x.
12
1
3


24. If sin A  , cos B 
, where  A   , and 0  B  , find the following: (i) tan  A  B 
2
2
2
2
(ii) tan  A  B  .
x
1
x
x
25. If sin x  , x in II quadrant , find the value of sin   , cos   , tan   .
4
2
2
2
x
x
x
4
, cos and tan , when tan x   , x lies in IInd quadrant.
2
2
2
3
 15  
 31 
27. Find the value of the trigonometric function: (i) cot  
 , (ii) sin 
.
4 

 3 
26. If 0  x  2 , find sin
13
1

and cos   , where ,  are acute angles, show that     .
14
7
3

29. If A  B  , prove that (i) 1  tan A1  tan B   2 , (ii)  cot A  1 cot B  1  2
4
28. If cos  
30. If tan       n tan      , show that  n  1 sin 2   n  1 sin 2
31. If sec   tan   p obtain the values of sec , tan  and sin  in terms of p.
a sin   b cos  a 2  b 2
a
, show that

b
a sin   b cos  a 2  b2
m
1

33. If tan  
and tan  
, prove that    
m 1
2m  1
4
32. If tan  
6
6
34. If sin   cos   m , then prove that sin   cos  
4  3  m 2  1
2
, where m 2  2
4
35. If tan  A  B   x and tan  A  B   y , find the values of tan 2 A and tan 2 B .
*Regular Assignments *Periodic Tests * Online live class * Guaranteed Results
Classes for- 10th,11th ,12th Engg.Entrance Exam. B.com(H/P),Eco(H),CA,CPT,QT, BBA, MBA
Mohanty Classes
Mob-9971649020 , B-1,Vasant Kunj,ND-70, www.mohantyclasses.com
2
2
36. If cos A  sin B  m and sin A  cos B  n , Prove that 2sin  A  B   m  n  2 .
3 tan x  tan 3 x

2 



tan
x


3
,
Prove
that
1



3
3 
1  3 tan 2 x


m
1

38. If tan A 
and tan B 
,then prove that A  B 
m 1
2m  1
4
 A B 
39. If cos ecA  sec A  cos ecB  sec B ,Prove that tan A.tan B  cot 
.
 2 
37. If tan x  tan  x 
40. Find the value of cot 2 + cosec
41. tan
+3tan2
11
4 3

17  3  4 3
 2 sin
 cos ec 2  4 cos 2

3
6 4
4
6
2

 
 
  
sin 180    cos  90    tan  270    cot  360   
1
42. tan 2250 cot 4050  tan 7650 cot 6750  0
0
43.
sin  360    cos  360    cos ec    sin  270   


 


    1  cot   sec       2 cot 
2
 
2

44. 1  cot   sec 

45.
tan  90    sec 180    sin   
sin 180    cot  360    cos ec  90   
1
5
 1
sin 
12
12 2
5
 1
47. 2 cos
cos 
12
12 2
46. 2sin
5

32
cos 
12
12
2
0
0
cos 55  cos 65  cos1750  0
5
4

sin
 cos
 3 sin
18
9
9

9
3
5
2 cos cos
 cos  cos
0
13
13
13
13

3
5
7 3
cos 4  cos 4
 cos 4
 cos 4

8
8
8
8 2

3
5
7 3
sin 4  sin 4
 sin 4
 sin 4

8
8
8
8 2


7
4
sin 2  sin 2  sin 2
 sin 2
2
18
9
18
9

3
5
7
sin 2  sin 2
 sin 2
 sin 2
2
8
8
8
8
48. 2sin
49.
50.
51.
52.
53.
54.
55.
*Regular Assignments *Periodic Tests * Online live class * Guaranteed Results
Classes for- 10th,11th ,12th Engg.Entrance Exam. B.com(H/P),Eco(H),CA,CPT,QT, BBA, MBA