Some time ago I encountered in my work a diophantine equation of the form

$A .cos(\frac{2 \pi k}{l} )= B$

For $A$ rational , $k ,l$ integers and $B$ irrational . The problem is already solved for $B$ rational in a somewhat more complicated looking diophantine equation. Now, my question is: What can be said in general about the solvability / solutions of this?