Explanation

(b) $\mu = \frac{\sin\left( \frac{A + \delta_{m}}{2} \right)}{\sin\frac{A}{2}}$
$\cot{\frac{A}{2} = \frac{\sin\left( \frac{A + \delta_{m}}{2} \right)}{\sin\frac{A}{2}}}$
Or $\ \ \frac{\cos\frac{A}{2}\ }{\sin\frac{A}{2}} = \frac{\sin\left( \frac{A + \delta_{m}}{2} \right)}{\sin\frac{A}{2}}$
Or $\ \ \sin{\left( \frac{\pi}{2} - \frac{A}{2} \right) = \sin\left( \frac{A + \delta_{m}}{2} \right)}$
Or $\frac{\pi}{2} - \frac{A}{2} = \frac{A}{2} + \frac{\delta_{m}}{2}$
Or $\frac{\pi}{2} - A = \frac{\delta_{m}}{2}$
$\frac{\pi - 2A}{2} = \frac{\delta_{m}}{2}$
$\therefore{\ \delta}_{m} = 180{^\circ} - 2A$