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Byju's Answer
Standard XII
Mathematics
Cosine Rule
In Δ ABC , if...
Question
In
Δ
ABC
,
if
(
a
+
b
+
c
)
(
a
−
b
+
c
)
=
3
ac
,
then
∠
B
=
.
A
π
4
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B
π
6
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C
π
2
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D
π
3
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Solution
The correct option is
D
π
3
(
a
+
b
+
c
)
(
a
−
b
+
c
)
=
3
ac
⇒
(
a
+
c
)
2
−
b
2
=
3
ac
or
a
2
+
c
2
−
b
2
=
ac
Also
,
cos
B
=
a
2
+
c
2
−
b
2
2
ac
=
1
2
⇒
∠
B
=
π
3