How do you evaluate cot(arcsin(x-1)) without a calculator?

##sqrt(2x-x^2)/(x-1) x in [0 2]##
Let ##a =arc sin ( x – 1 ) in [-pi/2 pi/2]##.
Then ##sin a = x-1 in [-1 1] to x in [0 2]##.
The given expression
##cot a = cos a/sin a=sqrt (1-sin^2a)/sin a=sqrt(1-(x-1)^2)/(x-1)=sqrt(2x-x^2)/(x-1)##