I am taking a calculus exam in less than one week, and I've stumbled upon this expression.
$$\lim\limits_{(x,y)\rightarrow(1,1)} \frac {\sin(x) - \sin (y)} {x-y}$$
Which I know to be cos(1), but I cannot seem to find the inequalities to make an $\epsilon-\delta$ proof of said limit.
I've tried coordinate change and Taylor, to no avail. Whenever I do Taylor(1) or equivalent infinitesimals, any variable I have manages to cancel out. If I don't, the thing just grows and grows...
Is there something I am entirely missing from the start?