Are there any angles x and y that satisfy sin(x+y)=sinx+siny?

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!

squares, rhombus, rectangles