I have got the solution for the V function, but I cannot have got the solution for the V2 function!
The Mathcad Prime 5 sheet in attach!
Maybe this helps:
The numeric solve (using root() ) shows one resul that looks very much like it is pi... See attached.
The numeric solve (using root() ) shows one resul that looks very much like it is pi..
For symmetry reasons one solution MUST be exact pi. Unfortunately alpha=pi leads to a local minimum, not a maximum.
Of course the two solutions 2.04 and 4,25 are symmetrical around pi and add up tp 2*pi.
Its too demanding for the symbolics.
Even Wolfram returns a numeric result only (apart from local minimum pi) - at least with just standard computation time:
I find old solution from my coauthor Victor Korobov - only Mathcad 11!
Can you do it in Mathcad 15?
Here you are. A simple assume statement does the trick and, Heureka!, you also get the symbolic solution!!!
The assume statement itself is ignored (we also get solutions greater than 2 pi) and there is a somewhat strange behavior of the result when it comes to plotting (using the values for the vertical markers) which makes necessary a redefinition of alpha.opt which I don't understand.