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 :

μ=sin(A+δm/2)/sin(A/2)
Given that μ = cot(A/2)
cot(A/2) = sin(A+δm/2)/sin(A/2)
cos(A/2)/sin(A/2) = sin(A+δm/2)/sin(A/2)
cos(A/2) = sin(A+δm/2)
sin(90-A/2) = sin(A+δm/2)
90-A/2 = A+δm/2
90 = 3A/2 + δm/2
180 = 3A + δm
δm = 180 - 3A
This option is not given.
Let's use another approach.
μ = sin[(A+δm)/2]/sin(A/2)
cot(A/2) = sin[(A+δm)/2]/sin(A/2)
cos(A/2)/sin(A/2) = sin[(A+δm)/2]/sin(A/2)
cos(A/2) = sin[(A+δm)/2]
sin(π/2 - A/2) = sin[(A+δm)/2]
π/2 - A/2 = (A+δm)/2
π - A = A + δm
δm = π - 2A = 180 - 2A