Verify the identity. $(Simplifyat$ each step.$)$

$tan(si{n}^{-1}(\frac{x-1}{2}))=\frac{x-1}{\sqrt[\phantom{2}]{4-(x-1{)}^2}}$

Let $=si{n}^{-1}(\frac{x-1}{2})=>sin()=\frac{x-1}{2}.$

$tan(si{n}^{-1}(\frac{x-1}{2}))=tan()$

$=\frac{2}{\frac{\sqrt[\phantom{2}]{4-(x-1{)}^2}}{2}}$

$=\frac{x-1}{\sqrt[\phantom{2}]{4-(x-1{)}^2}}$