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Mathematics
Mathematics
Problem
If
A
+
B
+
C
=
180
∘
A + B + C = 180^\circ
A
+
B
+
C
=
18
0
∘
,
sin
2
A
+
sin
2
B
+
sin
2
C
sin
A
+
sin
B
+
sin
C
=
k
sin
A
2
\frac{\sin 2A + \sin 2B + \sin 2C}{\sin A + \sin B + \sin C} = k \sin \frac{A}{2}
s
i
n
A
+
s
i
n
B
+
s
i
n
C
s
i
n
2
A
+
s
i
n
2
B
+
s
i
n
2
C
=
k
sin
2
A
sin
B
2
sin
C
2
\sin \frac{B}{2} \sin \frac{C}{2}
sin
2
B
sin
2
C
then the value of
3
k
3
+
2
k
2
+
k
+
1
3k^3 + 2k^2 + k + 1
3
k
3
+
2
k
2
+
k
+
1
is equal to
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