Napier's Analogy (Tangent Rule)

Rarely Tested
$$ \tan \left( \frac{A-B}{2} \right) = \frac{a-b}{a+b} \cot \frac{C}{2} $$
$$ \tan \left( \frac{B-C}{2} \right) = \frac{b-c}{b+c} \cot \frac{A}{2} $$
$$ \tan \left( \frac{C-A}{2} \right) = \frac{c-a}{c+a} \cot \frac{B}{2} $$
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