The refracting angle of prism is A and refractive index of material of prism is $\cot\frac{A}{2}$. The angle of minimum deviation is

180°-2A

$ \mu = \frac{sin(\frac{A+\delta_{min}}{2})}{sin\frac{A}{2}} = cot \frac{A}{2}$

$ \Rightarrow sin(\frac{A+\delta_{min}}{2}) = cos\frac{A}{2} = sin(90 -\frac{A}{2}) $

$ \frac{A+\delta_{min}}{2} = \frac{180 -A }{2}$

$\Rightarrow \delta_{min} = 180 -2A$