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Mathematics
Mathematics
Problem
Prove that for any real numbers
a
,
b
,
c
a,\,b,\,c
a
,
b
,
c
,
sin
a
+
sin
b
+
sin
c
−
sin
(
a
+
b
+
c
)
=
4
sin
a
+
b
2
sin
b
+
c
2
sin
c
+
a
2
.
\sin a+\sin b+\sin c-\sin(a+b+c)=4\sin\frac{a+b}{2}\,\sin\frac{b+c}{2}\,\sin\frac{c+a}{2}.
sin
a
+
sin
b
+
sin
c
−
sin
(
a
+
b
+
c
)
=
4
sin
2
a
+
b
sin
2
b
+
c
sin
2
c
+
a
.
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