Answer
$\frac{1}{2}[sin(10x)+sin(4x)]$
Work Step by Step
Using the Product-to-Sum Formula $sin(u)cos(v)=\frac{1}{2}[sin(u+v)+sin(u-v)]$, we have $sin(7x)cos(3x)=\frac{1}{2}[[sin(7x+3x)+sin(7x-3x)]=\frac{1}{2}[sin(10x)+sin(4x)]$
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