Mohanty Classes ( )

Mohanty Classes
Mob-9971649020 , B-1,Vasant Kunj,ND-70, www.mohantyclasses.com
SUMS ON INVERSE TRIGO
Find the principal value of :1
2
3
4
5
6
2

cos 1  cos
3

OD]
2

1 
  sin  sin
3


2
.[2009-C,D]
3
 8 
14 tan 1  x  2   tan 1  x  2   tan 1   ; x  0
 79 
[2010-C]
13 tan 1 x  2 cot 1 x 

 .[11

 1 
sin   sin 1     .[2011-D]
 2 
3
[2008-D]
7 

cos 1  cos
 .[2011-D], [2009-OD]
6 



3  
cos  cos 1  
   .
2

 6 


If tan 1 x  tan 1 y  , where xy  1 ,
4
find the value of x  y  xy .[2012-C]

7
cosec-1(cosec )  tan 1 (tan ) ?
6
6
Write in simpliest form: 1  sin x  1  sin x 
 [07-D]
1

sin
x

1

sin
x


 sin x  cos x 
,
16 Simplify:sin-1 
2




 x .
4
4
15 tan 1 

17 cot 1


1  x 2  x .[2007-D]

 cos x  sin x  
,   x 
4
 cos  sin x  4
18 tan 1 
Find the value of x :7
8

 x 1 
1  x  1 
  tan 
 ,
 x2
 x2 4
find the value of x. [2010-D], [2008OD], [2008-D], [2009-C,D]
If tan 1 
If tan 1 x  tan  1 y  tan 1 z   ,
show that x  y  z  xyz.
9
2 tan 1  cos x   tan 1  2 cos ec x 
[2009-OD]

 0, x  0.
3

11 sin 1 (1  x )  2 sin 1 x  . Hence,
2
verify the roots.
 1 x  1
1
12 tan 1 
  tan x  0; x  0
1

x
2


10 sin  1 2x  sin 1 x 
.[2009-C,OD], [2008-C,D]
Prove that:1
5 2
1 
 sec 1
 2 tan 1 
5
7
8 4
 cos x   x
  
20 tan 1 
   , x , 
 1  sin x  4 2
 2 2
19 2 tan 1
[2012-D]
3
3
6

 cot 1  
[125
2  5 13

OD]
[2010-OD]
4
 5
 16  
22 sin 1    sin 1    sin 1   
5
 13 
 65  2
21 cos  sin 1
.[2009-D]
1  x 

1
23 tan 1 
  4  tan x , 0  x  1.
1

x


[2008-C,D]
*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
35 Prove: sec2 (tan-12) + cosec2 ( cot-13) =
 1  x 2  1 x 2  
1
1
1 2
   cos x
24 tan 
15.
 1  x 2  1  x 2 
,
1
2
4
2
36 If cos 1 x  cos 1
 x 1
2
37
.[2011-D], [2009-OD]

1  x2
sin  cot 1 x   

2  x2


[2010-OD]
1
 1 x 
x  cos 1 
 , x   0,1
2
1 x 
[2010-D]
28 tan 1
29 tan
1
-
1
(2cosecx)
39 Solve for x:
sin 1 (1  x )  2 sin 1 x 

. Hence,
2
verify the roots.
40 Prove that :
a
a  2b
 1
 1
tan  cos 1   tan  cos 1  
b
b a
4 2
4 2
41 Show that sin
–1
+ cos- 1 + tan –1
= π
42 Evaluate
.[2010-D]
sin  2sin 1 0.6 
Ans:-
0.96
 1  cos x  1  cos x 
30 tan 
=
 1  cos x  1  cos x 
 x

4 2
43 Evaluate (i)
-1
9 9 1  1  9 1  2 2 
 sin    sin 
 3 
8 4
 3 4


.[2007-OD]
 3 
-1
32 Find the value of Sin ( sin 
 )
 5 
31
3
tan 2  tan 3 
4
1
1
34 Evaluate:tan-1 3 - sec-1 (-2) + cosec-1
2
.
3
2
Solve sin 1 x  sin 1 (1  x)  cos 1 x
1
1  tan  2  tan  3  
33 Prove that
2
-1
 1  sin x  1  sin x  x
 
  , x   0, 
 4
 1  sin x  1  sin x  2
1
=  show that
38 Solve the equation 2tan (cosx) = tan
26 cot 1 
27 cos  tan
3
9x - 12xy cos  +4y =36 sin 
 1 x  1 x   1
1
25 tan 1 
   cos x
 1 x  1 x  4 2
1

 x  1 .[11-OD]
2
1
y
2
44
sin 1  sin10 
ans:-
3  10
cos 1  cos10  ans- 4  10
45 Prove that
 cos   cos 
cos 1 
 1  cos  cos 



1 
  2tan  tan 2 tan 2 



46. Find x, if tan-13 + tan-1x = tan-18
47. Solve
for
x
:

 0, x  0.
3
1
48. Find the value of tan
[sin–1
2
1  y2
2x
–1
+ cos
],
1  y2
1  x2
sin  1 2x  sin 1 x 
*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
-1
49. If two angles of a triangle are tan 2
and tan-1 3, prove that the third angle
is π/4.
50. Solve
for x:
+
=2
*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 ( )

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