Answer
$\sin 2\theta =\dfrac {2\tan \theta }{1+\tan ^{2}\theta }$
Work Step by Step
$\sin 2\theta =2\sin \theta \cos \theta =2\dfrac {\tan \theta }{\sqrt {1+\tan ^{2}\theta }}\times \dfrac {1}{\sqrt {1+\tan ^{2}\theta }}=\dfrac {2\tan \theta }{1+\tan ^{2}\theta }$
