Limiting case for an angle in an equation

[Xsnac]

Homework Statement

Homework Equations

The one in the middle with cot (big tetha)

The Attempt at a Solution

I have no ideea how he finds the limiting cases for V<v0; v0<V and for V> v0/sqrt (1-v0^2) .
The problem is from Landau course for theoretical physics, volume 2: The Classical Theory of Fields. page 35.
I have been struggling with this problem for quite some time but made no real progress. Any bit of advice or even a full derivation step by step would be much appreciated. Is not a homework in the real sense btw. Thank you.

 

[TSny]

What is the independent variable for finding the extrema of

?

 

[Xsnac]

What is the independent variable for finding the extrema of
View attachment 108463
?

I would say the independent variable is tetha_0 since for each case we set V and V0 constant.

 

[TSny]

I would say the independent variable is tetha_0 since for each case we set V and V0 constant

Yes. Did you try finding the extrema of the right-hand side of the cotΘ expression?