Problem: Find all (x, y) such that sin x + sin y = sin (x+y) and |x| + |y| = 1
|x| + |y| =1 is easier to plot. We have to treat the cases separately.
- First quadrant: x +y = 1
- Second quadrant: -x + y = 1 (since |x| = -x when x is negative)
- Third Quadrant: -x-y =1
- Fourth Quadrant: x – y =1
Now we work on sin x + sin y = sin (x + y).