Examsnet
Unconfined exams practice
Home
Exams
Banking Entrance Exams
CUET Exam Papers
Defence Exams
Engineering Exams
Finance Entrance Exams
GATE Exam Practice
Insurance Exams
International Exams
JEE Exams
LAW Entrance Exams
MBA Entrance Exams
MCA Entrance Exams
Medical Entrance Exams
Other Entrance Exams
Police Exams
Public Service Commission (PSC)
RRB Entrance Exams
SSC Exams
State Govt Exams
Subjectwise Practice
Teacher Exams
SET Exams(State Eligibility Test)
UPSC Entrance Exams
Aptitude
Algebra and Higher Mathematics
Arithmetic
Commercial Mathematics
Data Based Mathematics
Geometry and Mensuration
Number System and Numeracy
Problem Solving
Board Exams
Andhra
Bihar
CBSE
Gujarat
Haryana
ICSE
Jammu and Kashmir
Karnataka
Kerala
Madhya Pradesh
Maharashtra
Odisha
Tamil Nadu
Telangana
Uttar Pradesh
English
Competitive English
Certifications
Technical
Cloud Tech Certifications
Security Tech Certifications
Management
IT Infrastructure
More
About
Careers
Contact Us
Our Apps
Privacy
Test Index
JEE Main Math Class 12 Inverse Trigonometric Functions Questions
Show Para
Hide Para
Share question:
© examsnet.com
Question : 22
Total: 74
For
k
∈
ℝ
, let the solutions of the equation
cos
(
sin
−
1
(
x
cot
(
tan
−
1
(
cos
(
sin
−
1
x
)
)
)
)
)
=
k
,
0
<
|
x
|
<
1
√
2
be
α
and
β
, where the inverse trigonometric functions take only principal values. If the solutions of the equation
x
2
−
b
x
−
5
=
0
are
1
α
2
+
1
β
2
and
α
β
, then
b
k
2
is equal to ________.
[27-Jul-2022-Shift-1]
Your Answer:
Validate
Solution:
cos
(
sin
−
1
(
x
cot
(
tan
−
1
(
cos
(
sin
−
1
)
)
)
)
=
k
.
⇒
cos
(
sin
−
1
(
x
cot
(
tan
−
1
√
1
−
x
2
)
)
)
=
k
⇒
cos
(
sin
−
1
(
x
√
1
−
x
2
)
)
=
k
⇒
√
1
−
2
x
2
√
1
−
x
2
=
k
⇒
1
−
2
x
2
1
−
x
2
=
k
2
⇒
1
−
2
x
2
=
k
2
−
k
2
x
2
∴
x
2
−
(
k
2
−
1
k
2
−
2
)
=
0
╱
α
╲
β
1
α
2
+
1
β
2
=
2
(
k
2
−
2
k
2
−
1
)
.
.
.
.
.
.
(
1
)
and
α
β
=
−
1
.
.
.
.
.
.
(2)
∴
2
(
k
2
−
2
k
2
−
1
)
(
−
1
)
=
−
5
⇒
k
2
=
1
3
and
b
=
S
⋅
R
=
2
(
k
2
−
2
k
2
−
1
)
−
1
=
4
∴
b
k
2
=
4
1
3
=
12
© examsnet.com
Go to Question:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
Prev Question
Next Question
Examsnet