Simplifying atan(tan(a+b))

Question

I wonder why this doesn't work as expected:

assume(x+y < %pi/2);
assume(x+y > -%pi/2);
atan(tan(x+y));

It reduces to:

atan(tan(x+y))

i.e. not at all. I would have expected it to reduce to:

x+y

Answer 1

Try triginverses.

(%i9) atan (tan (x + y));
(%o9)                          atan(tan(y + x))
(%i10) %, triginverses=all;
(%o10)                               y + x