Question

Is it ever possible that sin (A+B)=⁡ (A+B)= sin⁡ A+sin⁡ B?

Answer 1

Although this isn't obviously a general rule, you can choose the special case $A=B=0$, and the expression will become true:

$\sin(0+0)=0+0=\sin(0)+\sin(0)$

because all these expressions return 0.