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Byju's Answer
Standard VII
Mathematics
Angle Sum Property
In ABC prov...
Question
In
△
A
B
C
prove that
sin
(
B
−
C
2
)
=
(
b
−
c
2
)
cos
A
2
.
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Solution
A
B
C
is a triangle.
∴
A
+
B
+
C
=
π
⇒
sin
A
a
=
sin
B
b
=
sin
C
c
=
k
⇒
2
cos
(
B
+
C
2
)
sin
(
B
−
C
2
)
=
(
b
−
c
)
k
⇒
2
sin
(
A
2
)
sin
(
B
−
C
2
)
=
(
b
−
c
)
k
⇒
sin
A
=
a
k
⇒
2
sin
A
2
cos
A
2
=
a
k
⇒
sin
(
B
−
C
2
)
cos
(
A
2
)
=
(
b
−
c
a
)
∴
sin
(
B
−
C
2
)
=
(
b
−
c
a
)
cos
(
A
2
)
Hence Proved
Suggest Corrections
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Similar questions
Q.
In
△
A
B
C
prove that
sin
(
B
−
C
2
)
=
(
b
−
c
a
)
cos
A
2
Q.
Prove that
s
i
n
(
2
A
+
B
)
s
i
n
A
−
2
c
o
s
(
A
+
B
)
=
s
i
n
B
s
i
n
A
Q.
In triangle
A
B
C
prove that
i.
sin
A
=
sin
(
B
+
C
)
ii.
sin
2
A
=
−
sin
(
2
B
+
2
C
)
iii.
cos
A
=
−
cos
(
A
+
B
)
iv
tan
A
+
B
2
=
−
cot
C
2
Q.
Prove that
sin
(
B
−
C
2
)
=
b
−
c
a
cos
A
2
Q.
If
A
,
B
and
C
are the interior angles of a triangle
A
B
C
, Prove that:
cos
B
+
C
2
cos
C
+
A
2
cos
A
+
B
2
sin
A
2
sin
B
2
sin
C
2
=
1
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