The sum of tangents trigonometric identity gives us that
By letting and , the equivalent trigonometric identity on is
Given that the arctangent function is restricted to the principle branch of . What is the actual domain for the arctangent identity? Can you find sufficient and necessary conditions? How do we show that these conditions are indeed sufficient and necessary?
This question arose from observing comments in Trigonometry Paradox, and seeing that various people had different sets which they felt would work. For example:
Derek - .
Heli - .
Aditya - Sum of LHS lies in range.