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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Half Angles
In Δ ABC ...
Question
In
Δ
ABC
(
c
o
t
a
2
+
c
o
t
b
2
)
(
a
s
i
n
2
b
2
+
b
s
i
n
2
A
2
)
=
A
cot
C
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B
c
cot
C
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C
cot
C
2
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D
c
cot
C
2
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Solution
The correct option is
D
c
cot
C
2
[
S
(
S
−
a
)
△
+
S
(
S
−
b
)
△
]
[
a
(
S
−
c
)
(
S
−
a
)
a
c
+
b
(
S
−
b
)
(
S
−
c
)
b
c
]
=
S
△
[
c
]
×
1
c
[
2
S
2
−
S
(
a
+
c
+
b
+
c
)
+
a
c
+
b
c
]
=
S
△
[
2
S
2
−
S
(
2
S
+
c
)
+
c
(
a
+
b
)
]
=
S
/
△
[
2
S
2
−
2
S
2
−
S
c
+
c
(
2
S
−
c
)
]
=
S
/
△
[
−
S
c
+
2
S
c
−
c
2
]
=
S
/
△
[
S
c
−
c
2
]
=
S
c
△
[
S
−
c
]
=
c
(
S
(
S
−
c
)
△
)
=
c
c
o
t
c
/
2
⇒
(
D
)
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0
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In
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A
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prove that
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t
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t
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A
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