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Byju's Answer
Standard XII
Mathematics
Inverse Function
Considering p...
Question
Considering principal values, the number of solutions of
tan
−
1
2
x
+
tan
−
1
3
x
=
π
4
is
A
two
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B
three
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C
one
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D
none of these
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Solution
The correct option is
C
one
Given,
tan
−
1
(
2
x
)
+
tan
−
1
(
3
x
)
=
π
4
tan
−
1
(
5
x
1
−
6
x
2
)
=
π
4
Taking
t
a
n
on both the sides, we get
5
x
1
−
6
x
2
=
1
5
x
=
1
−
6
x
2
6
x
2
+
5
x
−
1
=
0
6
x
2
+
6
x
−
x
−
1
=
0
(
6
x
−
1
)
(
x
+
1
)
=
0
x
=
−
1
and
x
=
1
6
.
By considering the principal values, only
x
=
1
/
6
is possible
Hence there will be one real value of
x
.
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0
Similar questions
Q.
Considering only the principal values of inverse functions, the set
A
=
{
x
≥
0
:
tan
−
1
(
2
x
)
+
tan
−
1
(
3
x
)
=
π
4
}
Q.
The number of solutions of the equations
tan
−
1
2
x
+
tan
−
1
3
x
=
π
4
is
Q.
Inverse circular functions,Principal values of
s
i
n
−
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x
,
c
o
s
−
1
x
,
t
a
n
−
1
x
.
t
a
n
−
1
x
+
t
a
n
−
1
y
=
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
<
1
π
+
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
>
1
.
(a) Solve the equation
t
a
n
−
1
2
x
+
t
a
n
−
1
3
x
=
n
π
+
(
π
/
4
)
.
(b) Find all the positive integral solutions of
t
a
n
−
1
x
+
c
o
s
−
1
(
y
√
1
+
y
2
)
=
s
i
n
−
1
(
3
√
10
)
Q.
Considering only the principal values of inverse functions, the set
A
=
{
x
≥
0
:
tan
−
1
(
2
x
)
+
tan
−
1
(
3
x
)
=
π
4
}
Q.
Find the value of x which satisfy euqation :
tan
−
1
2
x
+
tan
−
1
3
x
=
π
/
4
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