Well the domain for that function will be all real x minus wherever there are asymptotes.
i.e. everywhere except when sinx+cosx=0
If you restrict it, a possible answer for the domain may be -π/4 < x < 3π/4
Lol, now I get why you asked for the general solution
Tbh, I don't know how I would express that, since it's a domain and not solutions to the equation.
I hope I helped in some way. Sorry if it didn't!
=]