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Byju's Answer
Standard XII
Mathematics
AM,GM,HM Inequality
Find the valu...
Question
Find the value of
cos
(
sec
−
1
x
+
cosec
−
1
x
)
,
|
x
|
≥
1.
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Solution
Given :
cos
(
sec
−
1
x
+
cosec
−
1
x
)
,
|
x
|
≥
1
∵
sec
−
1
x
+
cosec
−
1
x
=
π
2
,
|
x
|
≥
1
∴
cos
(
sec
−
1
x
+
cosec
−
1
x
)
=
cos
(
π
2
)
⇒
cos
(
sec
−
1
x
+
cosec
−
1
x
)
=
0
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0
Similar questions
Q.
Find the value of
cos
(
sec
−
1
x
+
c
o
s
e
c
−
1
x
)
,
|
x
|
≥
1
.
Q.
Number of value(s) of
x
satisfying sin
–1
x
+ cos
–1
x
+ sec
–1
x
+ cosec
–1
x
= π is
sin
–1
x
+ cos
–1
x
+ sec
–1
x
+ cosec
–1
x
= π को संतुष्ट करने वाले
x
के मान/मानों की संख्या है/हैं
Q.
Find the value of
cos
(
sec
−
1
x
+
csc
−
1
x
)
,
|
x
|
≥
1
Q.
Prove:
sin
−
1
(
1
x
)
=
c
o
s
e
c
−
1
x
,
∀
x
≥
1
or
x
≤
−
1
cos
−
1
(
1
x
)
=
sec
−
1
x
,
∀
x
≥
1
or
x
≤
−
1
tan
−
1
(
1
x
)
=
cot
−
1
x
,
∀
x
>
0
Q.
If
f
(
x
)
=
tan
−
1
x
−
cot
−
1
x
,
g
(
x
)
=
sec
−
1
x
−
cosec
−
1
x
,
h
(
x
)
=
sin
−
1
x
+
cos
−
1
x
+
tan
−
1
x
,
i
(
x
)
=
sin
−
1
x
−
cos
−
1
x
,
j
(
x
)
=
√
x
,
then
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AM,GM,HM Inequality
Standard XII Mathematics
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