PROBLEM SET
'tan is:
1. The principal value of sin 4
A
4 4 2 -
[WBJEE, 2008]
2. Value of tan -i| sin 2 1
Cos2
T
@-1
2
® 1- 4 C 2- 2 4
-1
4
[WBJEE, 2010]
3. If sin +cosec= 2 then the value of xis:
4 5 1 3
[AIEEE, 2007]
4. The value of cot cosec1+
3 +tan
tanequals: 3.
5
3 4
17 17 6
17 17
5. If x, y, z are in [AIEEE, 2008]
A.P. and tan-'x, tan-'y
also in A.P, then: and tan-z are
Inverse Circular Functions 229
2x =2y = 6z 6x = 3y =2z 16. tan+cos )+tan(-cos) is equal to:
© 6x = 4y = 3z x =y= Z
[AIEEE, 2013] A 2b b
a 2a
[WBJEE, 2009]
6. If fx) = 2tan'* +s i n x > 1, then f5) is
1+x
of the equation
equal to: 17. The most general solution
tan(secx})+cot(2cosx) =
(B) T are:
4tan-ls tan-/ 65
\156 2nnt 6
6
[Online JEE Main, 2015] 3
solution of the equation
18. The most general
7. Let tan'y = tan'x + tan where |x|<j5 sin[2 cos cot(2 tanx)]= 0
are:
then a value of y is: t1, t(1 + v2) 1, t(1 - V2)
3x- x 3* + x* 3x-x2 3x + x? -1, t(1 - V2)
1+ 3x? 1+3x2 1-312 1-3x? © +1, t(1 ± /2)
and y= sinx/1-y +i - ]
(JEE Main, 2015]
19. Forx= 2
8. The value of sin(-4x + 6) + cos(- 4x + 6)
for all xeR is: is equal to:
2 12
0 none of these 510 O none of these
12
9. If2 sin'x-3cos'x=4, then 2sin'x+3cos'x equals:
6T - 4 4- 6 3Tt 20. tanl+ tan2 + tan3 is equal to:
0 0
5 5 2 0
O none of these
10. If (cotx) - 7(cot'x) + 10 > 0, then x lies in the
interval:
(cot 5, cot 2) (-0, cot 5) U(cot 2, o) 21. If cot-(Vcos oa) - tan-"(Vcos a) =x, then sinx is
© (-0, cot 5) (cot 2, o) equal to:
11. The principal value of sinsin 3 is:
tan?
2 cot C) tan a. cota
A
2T
3 3 22. If sinx-+
none of these
3 ,0<<x|<v2, then x is equal to:
2
12. The value of tan +cos is: B 1 1 -1
3
5T
4
37
4
O none of these
23. The value of cos cos-+ is:
4 1
13. 2tan{cosec(tanx) -tan(cot'x)} is equal to: -1 none of these
n - tan'x
tan 24. The value of cos-)+ sin is:
tan'x n - cot'x
0
3
14. 2(sin'cos sin'x + cos'sin cos'x) is equal to: none of these
® 0 O 2x
30 30
15. sin cos'tan sec-'x (where x<V2) is equal to: 25. If sinx; = 15, then Sx, is equal to:
i=l
1
120 60 © 30 15
230
PARUL> Rudiments of Mathematics [MCQ for JEE Main!
26. If } cos-'x, = 0,
then x, is equal to: 37. If 0sA<, then
(k+ 1)
(3 2k k{k2-1) tan-tan 2A }+ tan(cotA) +tan(cot'A) is equal to.
2 k
0
27. The value of 4 2
is equal to: 38. If a =
sin-1l-x?
and B = 2
tan-1+x
1+x? 1-x0<*<1.
V3
2
2 then a+B is equal to:
2 2
28. If asin'x - bcos-lx = c
then asin-lx + bcosx is 0
equal to: 4 2
2
Tab + c(a + b) 39. cos-! 1+ l+ x (where x 0) is equal to:
a+b
Ttab - ca + b)
a+b V 2/1 +x?
© Tab + cla -b)
a+b
Tab +ca -b)
a-b
;tan'x tan-'x ©-cot'x
2 cot'x
29. If 3 sin'x - 4cos-'x = 4, then 40. The number of real solutions of the equation
4 sin-x + 3 cos'x is
equal to: V1+ cos2x = 2sinsin x), -nSx<I is:
0
(4-25n) © 2 none of these
©(4 + 251) none of these
41. If0 sa, b<land sin -1 2a
1+ a'
+ sin -1 2b = 2tan- x,
30. If sin'x + sin'y + cos'z = 2r, 1+b2
then x +y+ z is then x is equal to:
equal to:
ab a +b a+b at
0 B 3 2 1 1- ab 1- ab ab-1 ab -1
31. The value of sin[cot{tan(cosx)}} (where x >
0) is:
A
42. The value of tan sin(+cotis:
7 16 17
16
x
O none of these
32. If (sin'x)² + (cos-'x)' = -, x<0then xis equal to:
43. sin log, is defined for:
® -1
O1sxs9 ;sxs1 sxs9 0<xs9
44. If 2 tan-(cos ) = tan(2 cosec0), then is equal
to:
O none of these
2nT - © nT +
4 4 4
33. If tan-/x(x+1) +sin/x²+x+1 = , then x is 45. The value of
2
equal to: cosx + cos
0 0, -1 O 0, 1 -1
2Tt
34. cos tan-sin cot'x (where x > 0) is equal to:
x+1 lx+2 lx+1
none of these
x+2 x2+1 46. The solution of the equation
35. cot sin-'6x + sin-'6/3x=- is
-cot is equal to: 1
4 4
12
none of these
36. The value of tan-| X COS O, cot-'|_ cos is:
\1-xsin t/ lx- sin . 47. The number of solutions of the equation
independent ofa independent of x 2sin-'-x+1 + cos-!x?-x= 3 is
2
2 O3 1
Inverse Circular Functions 231
48, If a, b, c be positive real numbers, then:
58. If sin(tan'a), then a is equal to:
tan-!
bc +tan- a +b+c) 4 17--13²
ca
17 x13
+ tan -1 ca+b+c)
ab is equal to:
V17+132
2
59. If the three positive real numbers X, y, z (y < 1) are
A9. If = sin-'x+ cos'x- tan'x, x>0, then the smallest in G.P. and tan'x, tan-'y, tan'z are in A.P, then:
interval in which lies is given by: 1
3 x= y= Z
-s0s0 none of these
© x= y =Z=0
©0ses
4 60. The value of tan-| sin 2-1) is equal to:
cos2
50. a, Band y are three angles given by -1 2 2
a = 2tan(W2-1), B= 3sin1+ sin- and -1
©1 - 4
cog-
3 then:
61. cot+ cot+
2
cot1 2 t... tonterms is equal to:
a> B none of these tan-l_ 2n cot-. 2n
4n +5 4n +5
51. If cos'x + cosy + cos'z = 3r, then xy + yz + zx 2n cot-?. 2n
© tan 4n +3
is equal to: 4n +3
3 -3 O -1
62. If t a n = , then tant is equal to:
r=l
52. The value of coscos2+
3 sin(sin is equal to: 0 B 1
10 0
T
O none of these
3
)2 3 4
(UT, 2006]
3Tt
53. If sin-x + sin'y + sin'z = , then the value of 63. The number of positive integral solution(s) of the
+y' + - 3xyz is equal to: equation:
-6 6
tan'x + sec-1 yl
+y' = cosec-l VIO is
O0 none of these 3
54. cot(cosa + cos-b) + cot(sina + sin"b) is equal to: 2 ®0 1 4
2 4
64. The solution set of the inequation cosx < sin'x
is the interval:
55. If AABC is a right angled triangle with ZC=
then tan-!. + tan-!. is equal to: (-1, 1] (0, 1)
b+c C+a
[WBJEE, 2011]
B D0
2 4 4 65. If for two real numbers x, y withx<l andy s1
56. The number of solution(s) of the equation 1,
+ (sinx+ sin y) +, (sin-'x + sin- y
4 16
sin-12+ in-1 l2 ;is:
(sinx+sin- y) 2(8 - 3)
0 1 64 3(16+ 3r)
©2 O infinitely many thenthevalue of sin(1- y² +yI-*} is equal to:
2(32 + 157) 3T
57. } cos(k + is equal to:
k=l 3T 8 4
cot'2 O none to these
- 4
Rudiments of Mathematics [MCQ
for JEE Main ]
232 PARUL
66. 1f fz) - x(1331r 3630x 3300). then for
cos'(tan '(sinlcot 3))) of
a 75. The value
fta 1) - 31 2-5
sincot cos 4
O lim fx) = 1000 Ax)- 1000)dx =2500
67. If sin and tan 9 - P. then the value of
tan7 + tan-'5- cot-i-i is
sin
4s is equal to: 76. The value of
40
4
I+ (a B) none of these
77. The value of
68. The value of tan '2 4 cot is equal to: sinSOSC-1
cotcos a- tanvcos a+
37
4 4
O tan5 Onone of these
cot-(2-1) is:
69.
sn sin ) sin sin 13
2r| 78. The value of 2cos-'tan(2
0 -1
is equal to:
the value of
2T
79. If 3 + 5cos(2 cos'x + sin'x) =0, then
13 xis:
11
13
none of these 3
tan-3
70. If x = y= -7, then the value of lan l+ tan 2+
80. The value of cot1 +cot2 + cot-3 is:
2x
tan-!
1+ xy -sin' 1+ x + tan y is equal to:
2
21 © 2
0
D none of these 81. If 2k tan-!
I+ cos sec
cossec16
2
Cos-!l - 2
71. If0<a, b < 1, x> l and sin-4
-1 1 2x
1+g 1+b I+
4 tan- tan tan 32
then k =
= tan -2: then:
1
® 1 © 2 4
x =
a- b
1+ ab 82. If = +y+7, then
B tan
1+ ab
1+ ab
tan+ tan-1/x
b-a 2
© 2
tanx+ cot-! 4-b =
1+ ab
83. The value of tan2x?+ 3x + in-'2x?+ 3x +1
72. The solution set of x -4x < sin-'(sin 4) is: +cos-'4x + 4x+1 (for any real x) is:
(-, 2- V) ® (2-V, 2+ Wr) T 0
V, 2 +/r) (2+ V, o) 2
73. The value of sin 84. If a = 2cot(V2+1), B= 3sintsin
B
3' S= sinl
7
then:
74. The sum of the series a<ß<S<y 8<a<ß<y
cot2 + cot-'8 + cot'18 + cot32 + .. is: a<ô<ß<?
If fa)=tan(+}cosx)+tan(-cos'x)
1
85. 4 2 4 2
(x0), then the value of f is:
T
2 2 3
