c = Cos[phi]; s = Sin[phi]; ArcTan[c, s] // PowerExpand ArcTan[s/c] // PowerExpand
ArcTan[Cos[phi], Sin[phi]] phi
PowerExpand does not find its way with the two argument version of
ArcTan. However, it does with the single argument
ArcTan, as expected.
I like to use
ArcTan with two arguments since it does not suffer from division by zero unless numerator and denominator are zero.
How can I tell
PowerExpand to find its way into all inverse triginometric functions (assuming positive real variables, etc)?
What side effect would I suffer, if I attach a rule to
PowerExpand or better yet to inverse trigonometric functions to deal with
ArcTan[c, s] as
ArcTan[s/c]? What other identities around trigonometric and inverse trigonometric functions and the exponential function that would also fit such considerations?