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

Explanation

The refractive index (`mu`) of a prism of angle A and minimum deviation, `delta_(m)` is given by
`mu=sin((4+delta_(m))/2)/sin(A//2)`
Given, `mu=cos""A/2`
`therefore cot""A/2=sin((A+delta_(m))/2)/sin(A//2)`
`(cosA//2)/(sinA//2)=(sin""((A+delta))/2)/sin(A//2)rArrcos""A/2=sin((A+delta_(m))/2)`
`therefore sin(90^(@)-A/2)=sin((A+delta_(m))/2)`
`rArr90^(@)-A/2=(A+delta_(m))/2rArr180^(@)-A=A+delta_(m)`
`rArr` Angle of minimum deviation, `delta_(m)=180^(@)-2A=pi-2A`