Maximum angle of deflection after collision

[osy044]

Homework Statement

A smooth sphere A impinges obliquely on a stationary sphere B of equal mass. The directions of motion of sphere A before impact and after impact make angles α and β respectively with the line of centres at the instant of impact.

show that cotβ=((1-e)cotα)/2

where e is the coefficient of restitution.
Find in terms of α and e, the tangent of the angle through which the sphere A is deflected, and show that, if α is varied, this angle is the maximum when

tan^2 α=(1-e)/2

Homework Equations

conservation of momentum
coefficient of restitution law

The Attempt at a Solution

I have no problem with first part but the second part seems weird. I think its possible that tan^2 α<(1-e)/2. But anyway using this equation α + β always makes 90 degree. I am wondering if this makes the maximum angle of deflection. but i think they can be less than 90 to make much greater angle of deflection. Please explain it to me.

 

[osy044]

Please help me
im crying

tt.tt