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

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Answer 1 · 2016-11-27T06:47:38

$sqrt(2x-x^2)/(x-1), x in [0, 2]$

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

$cot a = cos a/sin a=sqrt (1-sin^2a)/sin a=sqrt(1-(x-1)^2)/(x-1)=sqrt(2x-x^2)/(x-1)$

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