Question 1209179
Note that since -1<=sin(x)<=1 for all x, -2<=sin(x)-1<=0 for all x, so |sin(x)-1|/(sin(x)-1)=(1-sin(x))/(sin(x)-1)=-1 for all x where sin(x) is not 1. This means that the limit at x=pi/2 is -1, since all the x-values close to it are always -1.