Another strange combination of things is
cos(x)/-cos(x), for x from -1 to 1 and back in a wave
and the like.
So apart from the obvious need to deal with 0 correctly, and as it only provides a sign in the equation, how do you know if one is required or missing?
Is m2 always positive? It is if we haven’t missed a cos(m)/-cos(m) out of the equation somehow. But then, we cannot always be sure if we have chosen correctly.