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?