I'm trying to find the following limit:
$ \lim_ {x \to 1} \frac{\sin{\pi x}}{1 - x^2} $
I can't figure it out how to reach the fundamental trigonometric limit. Everything i see is that the denominator is a difference between squares, and then can be factorated
$ \lim_ {x \to 1} \frac{\sin{\pi x}}{(1 - x)(1 + x)} $
I'd like to know how can i simplify this expression to eliminate the indetermination.