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)##