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Byju's Answer
Standard XI
Mathematics
Properties Derived from Trigonometric Identities
Sum to infini...
Question
Sum to infinite terms of the series
c
o
t
−
1
(
1
2
+
3
4
)
+
c
o
t
−
1
(
2
2
+
3
4
)
+
c
o
t
−
1
(
3
2
+
3
4
)
+
.
.
.
.
.
.
.
is
A
π
4
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B
t
a
n
−
1
2
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C
t
a
n
−
1
3
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D
c
o
t
−
1
3
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Solution
The correct option is
B
t
a
n
−
1
2
T
n
=
c
o
t
−
1
(
n
2
+
3
4
)
=
t
a
n
−
1
(
1
n
2
+
3
4
)
=
t
a
n
−
1
(
n
+
1
2
)
−
t
a
n
−
1
(
n
−
1
2
)
S
n
=
∑
n
n
=
1
t
n
=
t
a
n
−
1
(
n
+
1
2
)
−
t
a
n
−
1
1
2
⇒
S
∞
=
π
2
−
t
a
n
−
1
1
2
=
c
o
t
−
1
1
2
=
T
a
n
−
1
2
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Q.
Sum to infinite terms of the series
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