$\frac{s i n x - s i n y}{c o s x + c o s y} =$

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Solution

$\frac{s i n x - s i n y}{c o s x + c o s y} = \frac{2 c o s (\frac{x + y}{2}) s i n (\frac{x - y}{2})}{2 c o s (\frac{x + y}{2}) c o s (\frac{x - y}{2})}$

$= t a n (\frac{x - y}{2})$

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