cot(A/z) + cot(B/z) + cot(c/2) = (a + b + c)/(a + c - a) * cot(A/2)
You asked:
Investigate the equation: \(\cot\left( \frac{A}{z} \right) + \cot\left( \frac{B}{z} \right) + \cot\left( \frac{c}{2} \right) = \frac{a + b + c}{a + c - a} \cdot \cot\left( \frac{A}{2} \right)\).