\begin{eqnarray*}f'(x) &=& \cfrac{\sin x - x\cos x}{\sin^{2} x} - \sin x \\\\&=& \cfrac{\sin x - x\cos x - \sin^3 x}{\sin^2 x} \\\\&=& \cfrac{\sin x (1 - \sin^2 x)- x\cos x}{\sin^2 x} \\\\&=& \cfrac{\sin x (\cos^2 x)- x\cos x}{\sin^2 x} \\\\&=& \cfrac{\cos x　(\sin x \cos x- x)}{\sin^2 x} \\\\\end{eqnarray*}