The formula for refractive index of materaial of a prism is-

n=[sin(A+dm)/2]/sin(A/2)----(1)

dm=angle of minimum deviation.

Now, n=cot(A/2)=cos(A/2)/sin(A/2). Using this fact in eq.(1),

cos(A/2)=sin(A+dm)/2.

sin(90±A/2)=sin(A/2+dm/2)

Therefore,

90+A/2=A/2+dm/2. This gives dm=180.

This is not possible. Then,

90-A/2=A/2+dm/2. So,

(90-A)2=dm or

dm=180-2A