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Byju's Answer
Standard XII
Mathematics
Polar Representation of a Complex Number
In any triang...
Question
In any triangle ABC prove that the identities.
sin
2
A
+
sin
2
B
+
sin
2
C
cos
A
+
cos
B
+
cos
C
−
1
=
8
cos
(
A
/
2
)
cos
(
B
/
2
)
cos
(
C
/
2
)
.
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Solution
L.H.S.
=
4
sin
A
sin
B
sin
C
4
sin
(
A
/
2
)
sin
(
B
/
2
)
sin
(
C
/
2
)
=
8
cos
(
A
/
2
)
cos
(
B
/
2
)
cos
(
C
/
2
)
∵
sin
A
=
2
sin
(
A
/
2
)
cos
(
A
/
2
)
etc.
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0
Similar questions
Q.
lf
A
+
B
+
C
=
180
∘
. Match the following
List -I List -II
1.
cos
A
+
cos
B
+
cos
C
a.
2
+
2
cos
A
cos
B
cos
C
2.
sin
2
A
+
sin
2
B
+
sin
2
C
b.
4
cos
A
2
cos
B
2
cos
C
2
3.
sin
2
A
+
sin
2
B
+
sin
2
C
c.
1
+
4
sin
A
2
sin
B
2
sin
C
2
4.
sin
A
+
sin
B
+
sin
C
d.
4
sin
A
sin
B
sin
C
Q.
In any triangle ABC prove the identities.
sin
2
A
+
sin
2
B
−
sin
2
C
=
2
sin
A
sin
B
cos
C
.
Q.
In triangle ABC ,prove that
sin
2
A
2
+
sin
2
B
2
−
sin
2
C
2
=
1
−
2
cos
A
2
cos
B
2
s
i
n
C
2
Q.
If
A
+
B
+
C
=
0
, (Note
0
,
≠
π
) then prove that
sin
2
A
+
sin
2
B
+
sin
2
C
=
2
(
sin
A
+
sin
B
+
sin
C
)
(
1
+
cos
A
+
cos
B
+
cos
C
)
Q.
In any triangles ABC prove the identities.
cos
A
+
cos
B
+
cos
C
=
1
+
4
sin
(
A
/
2
)
sin
(
B
/
2
)
sin
(
C
/
2
)
.
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