I need to prove that $\lim\limits_{(x,y)\to (0,0)} \frac{\sin(xy)}{\sin(x)\sin(y)}$ exists using the $ϵ-δ$ limit definition as $(x,y)→(0,0)$.
I know that the limit exist and is equal to $1$. I worked on it using the squeeze theorem, but we didn't see it in class so I can't use it, the only thing I can use is the $ϵ-δ$ definition and I have no idea how to do it.