How do you evaluate ##cot(arcsin(x-1))## without a calculator?
February 20th, 2023
##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)##
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