Byju's Answer
Standard XII
Mathematics
Cosine Rule
Evaluate ∑s...
Question
Evaluate
∑
sin
(
C
−
A
)
sin
C
sin
A
if none of
sin
A
,
sin
B
,
sin
C
is zero.
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Solution
∑
sin
(
C
−
A
)
sin
C
sin
A
=
∑
sin
C
cos
A
−
cos
C
sin
A
sin
C
sin
A
=
∑
sin
C
cos
A
sin
C
sin
A
−
∑
cos
C
sin
A
sin
C
sin
A
=
∑
cos
A
sin
A
−
∑
cos
C
sin
C
=
∑
cot
A
−
cot
C
=
cot
A
−
cot
C
+
cot
C
−
cot
B
+
cot
B
−
cot
A
=
0
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0
Similar questions
Q.
If
A
+
B
+
C
=
π
, prove that
(
sin
A
+
sin
B
+
sin
C
)
(
−
sin
A
+
sin
B
+
sin
C
)
(
sin
A
−
sin
B
+
sin
C
)
(
sin
A
+
sin
B
−
sin
C
)
=
4
sin
2
A
sin
2
B
sin
2
C
.
Q.
In a triangle
A
B
C
, if
(
sin
A
+
sin
B
+
sin
C
)
(
sin
A
+
sin
B
−
sin
C
)
=
3
sin
A
sin
B
is equal to
Q.
If in a
△
A
B
C
,
(
sin
A
+
sin
B
+
sin
C
)
(
sin
A
+
sin
B
−
sin
C
)
=
3
sin
A
sin
B
,
then angle
C
(in degree) is
Q.
Prove:
sin
(
A
−
B
)
sin
A
sin
B
+
sin
(
B
−
C
)
sin
B
sin
C
+
sin
(
C
−
A
)
sin
C
sin
A
=
0
Q.
In
Δ
A
B
C
the sides opposite to angles
A
,
B
,
C
are denoted by
a
,
b
,
c
respectively.
If
(
sin
A
+
sin
B
+
sin
C
)
(
sin
A
+
sin
C
−
sin
B
)
=
μ
sin
A
sin
C
,
where
sin
A
=
a
k
,
sin
B
=
b
k
,
sin
C
=
c
k
then the range of
μ
is
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