Aus Online Mathematik Brückenkurs 1

When you cancel \displaystyle \tan x on both sides of the equation you might lose those solutions that satisfy \displaystyle \tan x=0. The equation to the right might therefore, potentially, have a reduced set of solutions. You should consequently use the \displaystyle \Leftarrow arrow.

NB. It doesn't matter that it later turns out that both equations do in fact have the same set of solutions. It is what you know at the time that determines what kind of arrow you use.