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Prove that: (sin A+sin B)/(sin A-sin B)=...

Prove that: `(sin A+sin B)/(sin A-sin B)=tan((A+B)/2)cot((A-B)/2)`

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To prove that \[ \frac{\sin A + \sin B}{\sin A - \sin B} = \tan\left(\frac{A+B}{2}\right) \cot\left(\frac{A-B}{2}\right) \] we will start by simplifying the left-hand side (LHS). ...
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