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Byju's Answer
Standard XII
Mathematics
Integration of Trigonometric Functions
If tan -1 1...
Question
If
tan
ā
1
1
ā
x
1
+
x
=
1
2
tan
ā
1
x
, then
x
=
A
1
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B
√
3
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C
1
√
3
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D
None of these
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Solution
The correct option is
C
1
√
3
tan
−
1
1
−
x
1
+
x
=
1
2
tan
−
1
x
⇒
2
tan
−
1
(
1
−
x
1
+
x
)
=
tan
−
1
x
⇒
tan
−
1
⎛
⎜ ⎜
⎝
2
(
1
−
x
1
+
x
)
1
−
(
1
−
x
1
+
x
)
2
⎞
⎟ ⎟
⎠
=
tan
−
1
x
⇒
2
(
1
−
x
)
(
1
+
x
)
(
1
+
x
)
2
−
(
1
−
x
)
2
=
x
⇒
2
(
1
−
x
2
)
4
x
=
x
⇒
2
−
2
x
2
=
4
x
2
⇒
2
=
6
x
2
⇒
x
=
1
√
3
Suggest Corrections
0
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