Question

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

Answer 1

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

Explanation:

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)`