The limit of LIM (1-x ^ 2) / sin Wu x when x approaches 1 Why not multiply a bounded function by infinitesimal and then equal 0

The limit of LIM (1-x ^ 2) / sin Wu x when x approaches 1 Why not multiply a bounded function by infinitesimal and then equal 0

Original formula = Lim [(1 + x) (1-x)] / (sin π x)
X - > 1 means 1-x - > 0,1 + X - > 2
Let t = 1-x
sinπx=sinπ(-t+1)=-sinπt-π=sinπt
The original formula = lim2t / sin π t
=lim(2/π)[πt/(sinπt)]=2/π