If
sin
(
x
+
y
)
−
sin
(
x
−
y
)
=
2
f
(
x
)
sin
y
,
\displaystyle {\sin{{\left({x}+{y}\right)}}}-{\sin{{\left({x}-{y}\right)}}}={2}{f{{\left({x}\right)}}}{\sin{{y}}},
sin
(
x
+
y
)
−
sin
(
x
−
y
)
=
2
f
(
x
)
sin
y
,
then
f
(
x
)
=
\displaystyle {f{{\left({x}\right)}}}=
f
(
x
)
=
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