$C=\dfrac{\sin x+\tan x}{\tan x-\sin x\cos x}$
$=\dfrac{\sin x+\tan x}{\dfrac{\sin x}{\cos x}-\sin x\cos x}$
$=\dfrac{\cos x(\sin x+\tan x)}{\sin x-\sin x\cos^2x}$
$=\dfrac{\sin x\cos x+\sin x}{\sin x(1-\cos^2x)}$
$=\dfrac{\sin x(\cos x+1)}{\sin x.\sin^2x}$
$=\dfrac{\cos x+1}{\sin^2x}$