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Tardigrade
Question
Mathematics
Let S = x ∈ R: 0< x< 1. and .2 tan -1((1-x/1+x))= cos -1((1-x2/1+x2)) . If n(S) denotes the number of elements in S then :
Q. Let
S
=
{
x
∈
R
:
0
<
x
<
1
and
2
tan
−
1
(
1
+
x
1
−
x
)
=
cos
−
1
(
1
+
x
2
1
−
x
2
)
}
. If
n
(
S
)
denotes the number of elements in
S
then :
607
141
JEE Main
JEE Main 2023
Inverse Trigonometric Functions
Report Error
A
n
(
S
)
=
2
and only one element in
S
is less than
2
1
.
0%
B
n
(
S
)
=
1
and the element in
S
is less than
2
1
.
100%
C
n
(
S
)
=
1
and the elements in
S
is more than
2
1
.
0%
D
n
(
S
)
=
0
0%
Solution:
0
<
x
<
1
2
tan
−
1
(
1
+
x
1
−
x
)
=
cos
−
1
(
1
+
x
2
1
−
x
2
)
tan
−
1
x
=
θ
∈
(
0
,
4
π
)
∴
x
=
tan
θ
2
tan
−
1
(
tan
(
4
π
−
θ
)
)
=
cos
−
1
(
cos
2
θ
)
2
(
4
π
−
θ
)
=
2
θ
∴
4
θ
=
2
π
∴
θ
=
8
π
x
=
tan
8
π
∴
x
=
2
−
1
≃
0.414