If either x or y or both are equal to 0, then the equation is satisfied.
CHECK [y = 0]:
sin(x+0) = sin x + sin 0
sin x = sin x Yup!
CHECK [x = 0]
sin(0+ y) = sin 0 + sin y
sin y = sin y Yup!
CHECK [x,y = 0]
sin (0+0) = sin 0 + sin 0
sin 0 = sin 0 Yup!
It all checks out! Hope that helps!