How to achieve a particular simplification level of an expression in wxMaxima?

Question

I have the following input in wxMaxima:

BC:(sqrt((L^2)-((R^2)*sin(α)^2))+R*cos(α))*tg(α)$
AC:(sqrt((L^2)-((R^2)*sin(α)^2)))/cos(α)$
v_B:ω*R*(BC/AC)$
v_B;

I get the desired result but it's in a quite complicated form. I would like to simplify it to this:

I tried various options from the Simplify menu (especially Trigonometric Simplification) but none of them gave me such a result. Is there a way to perform this kind of simplification in wxMaxima?