b
As \(\mu  = \frac{{\sin \left( {\frac{{A + \delta }}{2}} \right)}}{{\sin \left( {\frac{A}{2}} \right)}}\)

\(\cot \frac{A}{2} = \frac{{\sin \left( {\frac{{A + \delta }}{2}} \right)}}{{\sin \left( {\frac{A}{2}} \right)}}\)               \(\left[ {\because \mu  = \cot \frac{A}{2}} \right]\)

\(\frac{{\cos \left( {\frac{A}{2}} \right)}}{{\sin \,\,\left( {\frac{A}{2}} \right)}} = \) \(\frac{{\sin \left( {\frac{{A + \delta }}{2}} \right)}}{{\sin \,\,\left( {\frac{A}{2}} \right)}}\)

\(\sin \,\left( {\frac{\pi }{2} - \frac{A}{2}} \right)\,\) \( = \,\sin \,\left( {\frac{A}{2} + \frac{\delta }{2}} \right)\,;\)   \(\frac{\pi }{2} - \frac{A}{2}\, = \)  \(\frac{A}{2} + \frac{\delta }{2}\)

\(\therefore \delta  = \pi  - 2A = {180^o} - 2A\)