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JEE Main 27-Aug-2021 Shift 2 Solved Paper
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© examsnet.com
Question : 76
Total: 90
If
y
(
x
)
=
cot
−
1
(
√
1
+
sin
x
+
√
1
−
sin
x
√
1
+
sin
x
−
√
1
−
sin
x
)
,
x
∈
(
π
2
,
π
)
, then
d
y
d
x
at
x
=
5
π
6
is
[27 Aug 2021 Shift 2]
−
1
2
-1
1
2
0
Validate
Solution:
y
(
x
)
=
cot
−
1
(
√
1
+
sin
x
+
√
1
−
sin
x
√
1
+
sin
x
−
√
1
−
sin
x
)
,
x
∈
(
π
2
,
π
)
=
cot
−
1
|
cos
x
2
+
sin
x
2
|
+
|
cos
x
2
−
sin
x
2
|
|
cos
x
2
+
sin
x
2
|
−
|
cos
x
2
−
sin
x
2
|
=
cot
−
1
(
cos
x
2
+
sin
x
2
+
sin
x
2
−
cos
x
2
cos
x
2
+
sin
x
2
−
sin
x
2
+
cos
x
2
)
[
∵
x
2
∈
(
π
4
,
π
2
)
]
=
cot
−
1
(
sin
x
2
cos
x
2
)
=
cot
−
1
(
tan
x
2
)
=
cot
−
1
(
cot
(
π
2
−
x
2
)
)
⇒
y
(
x
)
=
π
2
−
x
2
∴
y
′
(
x
)
=
−
1
2
© examsnet.com
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