Question

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Answer 1

$\frac{Sin(\alpha+\beta)*Sin(\alpha-\beta)}{Sin\alpha+Sin\beta} =\frac{Cos(\alpha+\beta-\alpha+\beta)-Cos(\alpha+\beta+\alpha-\beta)}{2(Sin\alpha+Sin\beta)}=\frac{Cos2\beta-Cos2\alpha}{2(Sin\alpha+Sin\beta)}=\frac{1-2Sin^{2}\beta-1+2Sin^{2}\alpha}{2(Sin\alpha+Sin\beta)}=\frac{2(Sin^{2}\alpha-Sin^{2}\beta)}{2(Sin\alpha+Sin\beta) }=\frac{(Sin\alpha+Sin\beta)(Sin\alpha-Sin\beta)}{Sin\alpha+Sin\beta}=Sin\alpha-Sin\beta$