\displaystyle [br]\begin{equation*}\frac{\sqrt{1-\cos^2 \theta}}{\tan \theta} = \frac{\sin \theta}{\frac{\sin \theta}{\cos \theta}} = \sin \theta \times \frac{1}{\frac{\sin \theta}{\cos \theta}} = \sin \theta \times \frac{\cos \theta}{\sin \theta} = \cdots\end{equation*}
\displaystyle [br]\begin{equation*}\frac{\sqrt{1-\cos^2 \theta}}{\tan \theta} = \frac{\sin \theta}{\frac{\sin \theta}{\cos \theta}} = \sin \theta \times \frac{1}{\frac{\sin \theta}{\cos \theta}} = \sin \theta \times \frac{\cos \theta}{\sin \theta} = \cdots\end{equation*}
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