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MHT CET 2021 Math Solved Paper
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© examsnet.com
Question : 50
Total: 100
π
∕
2
∫
π
∕
6
c
o
s
e
c
x
⋅
cot
x
1
+
c
o
s
e
c
2
x
d
x
=
tan
−
1
2
tan
−
1
(
1
3
)
tan
−
1
1
π
4
−
tan
−
1
2
Validate
Solution:
Let
I
=
π
∕
2
∫
π
∕
6
c
o
s
e
c
x
⋅
cot
x
1
+
c
o
s
e
c
2
x
d
x
Let
c
o
s
e
c
x
=
t
⇒
−
c
o
s
e
c
x
cot
x
d
x
=
d
t
When
x
=
π
6
, then
t
=
c
o
s
e
c
π
6
=
2
and when
x
=
π
2
, then
t
=
c
o
s
e
c
π
2
=
1
∴
I
=
1
∫
2
−
d
t
1
+
t
2
=
−
1
∫
2
d
t
1
+
t
2
=
2
∫
1
d
t
1
+
t
2
=
[
tan
−
1
(
t
)
]
1
2
=
tan
−
1
(
2
)
−
tan
−
1
(
1
)
=
tan
−
1
(
2
−
1
1
+
2
×
1
)
=
tan
−
1
(
1
1
+
2
)
=
tan
−
1
(
1
3
)
© examsnet.com
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