Answer
$csc[arccos(x-1)]=\frac{1}{\sqrt {-x^2+2x}}$
Work Step by Step
Let $u=arccos(x-1)~~$ (Range: $0\lt u\lt\pi$)
Then: $x-1=cos~u$
$sin^2u+cos^2u=1$
$sin^2u=1-cos^2u$
$sin^2u=1-(x-1)^2=1-x^2+2x-1=-x^2+2x$
$sin~u=\sqrt {-x^2+2x}~~$ ($0\lt u\lt\pi$)
$csc[arccos(x-1)]=csc~u=\frac{1}{sin~u}=\frac{1}{\sqrt {-x^2+2x}}$
