به جای تانژانت آلفا $\frac{\sin \alpha }{\cos \alpha }$ را جاگذاری می‌کنیم: $\begin{align}  & \frac{\frac{\sin \alpha }{\cos \alpha }-\sin \alpha }{\frac{\cos \alpha }{1+\cos \alpha }}=\frac{\frac{\sin \alpha -\sin \alpha \cos \alpha }{\cos \alpha }}{\frac{\cos \alpha }{1+\cos \alpha }}=\frac{\frac{\sin \alpha (1-\cos \alpha )}{\cos \alpha }}{\frac{\cos \alpha }{1+\cos \alpha }} \\  & =\frac{\sin \alpha (1-\cos \alpha )(1+\cos \alpha )}{{{\cos }^{2}}\alpha }=\frac{\sin \alpha (\overbrace{1-{{\cos }^{2}}\alpha }^{{{\sin }^{2}}\alpha })}{{{\cos }^{2}}\alpha }=\frac{{{\sin }^{3}}\alpha }{{{\cos }^{2}}\alpha } \\ \end{align}$