$\int\frac{dx}{\sqrt{2x-x^2}}$ is equal to

sin–1 (1 - x) + c – cos–1 (1 – x) + c sin-1 (x – 1) + c cos-1 (x – 1) + c

sin-1 (x – 1) + c

Let $I=\int\frac{dx}{\sqrt{1-(x^2-2x+1)}}=\int\frac{dx}{\sqrt{1-(x-1)^2}}=sin^{-1}(\frac{x-1}{1})+c$. Hence (C) is the correct answer.