The refracting angle of a prism is A, and refractive index of the material of the prism is cot (A/2). The angle of minimum deviation is 

As, we know that  $\mu =\frac{\sin \left(\frac{A+D_m}{2}\right)}{\sin \frac{A}{2}}$

$$\begin{gathered} \Rightarrow \cot \frac{A}{2}=\frac{\sin \left(\frac{A+D_m}{2}\right)}{\sin \frac{A}{2}} \\ \Rightarrow \frac{\cos \frac{A}{2}}{\sin \frac{A}{2}}=\frac{\sin \left(\frac{A+D_m}{2}\right)}{\sin \frac{A}{2}} \\ \Rightarrow \sin (\frac{\pi }{2}-\frac{A}{2})=\sin \left(\frac{A+D_m}{2}\right) \\ \Rightarrow D_m=\pi -2A\Rightarrow D_m={180}^0-2A \end{gathered}$$