Answer
The expression on the left-side is equal to the expression on the right-side.
Work Step by Step
The given expression on the left side $\frac{\sin 2\theta }{1-{{\sin }^{2}}\theta }$ can be simplified by applying the double angle formula $\sin 2\theta =2\sin \theta \cos \theta $ and as per the Pythagorean Theorem ${{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1$; therefore, $1-{{\sin }^{2}}\theta ={{\cos }^{2}}\theta $. So, the expression will be:
$\begin{align}
& \frac{\sin 2\theta }{1-{{\sin }^{2}}\theta }=\frac{2\sin \theta \cos \theta }{{{\cos }^{2}}\theta } \\
& =\frac{2\sin \theta }{\cos \theta }.\frac{\cos \theta }{\cos \theta } \\
& =2\tan \theta .1 \\
& =2\tan \theta
\end{align}$
Hence, the expression on the left-side is equal to the expression on the right-side.
