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Mathematics
Problem
Show that the product of sines of the sum and difference of two angles can be written as
sin
(
x
+
y
)
sin
(
x
−
y
)
=
sin
2
x
−
sin
2
y
.
\sin(x+y)\,\sin(x-y)=\sin^{2}x-\sin^{2}y.
sin
(
x
+
y
)
sin
(
x
−
y
)
=
sin
2
x
−
sin
2
y
.
Provide a complete algebraic proof valid for all real
x
x
x
and
y
y
y
.
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