$\begin{align}  & \frac{1-\sin \theta +\cos \theta }{1-\sin \theta }=\frac{(1-\sin \theta +\cos \theta )\times (1+\sin \theta )}{(1-\sin \theta )(1+\sin \theta )} \\ & \frac{1-\sin \theta +\cos \theta }{1-\sin \theta }=\frac{1-\sin \theta +\cos \theta +\sin \theta -{{\sin }^{2}}\theta +\sin \theta \cos \theta }{1-{{\sin }^{2}}\theta } \\ & \frac{1-\sin \theta +\cos \theta }{1-\sin \theta }=\frac{1-{{\sin }^{2}}\theta +\cos \theta +\sin \theta \cos \theta }{1-{{\sin }^{2}}\theta } \\ & \frac{1-\sin \theta +\cos \theta }{1-\sin \theta }=\frac{{{\cos }^{2}}\theta +\cos \theta +\sin \theta \cos \theta }{{{\cos }^{2}}\theta } \\ & \frac{1-\sin \theta +\cos \theta }{1-\sin \theta }=\frac{\cos \theta (\cos \theta +1+\sin \theta )}{{{\cos }^{2}}\theta } \\ & \frac{1-\sin \theta +\cos \theta }{1-\sin \theta }=\frac{1+\cos \theta +\sin \theta }{\cos \theta } \end{align}$