Answer
$\sqrt {2}$
Work Step by Step
$\lim _{\theta \rightarrow \dfrac {\pi }{4}}\dfrac {\sin ^{2}\theta -\cos ^{2}\theta }{\sin \theta -\cos \theta }=\lim _{\theta \rightarrow \dfrac {\pi }{4}} \dfrac {\left( \sin \theta -\cos \theta \right) \left( \sin \theta +\cos \theta \right) }{\sin \theta -\cos \theta }=\lim _{\theta \rightarrow \dfrac {\pi }{4}}\left( \sin \theta +\cos \theta \right) =\sin \dfrac {\pi }{4}+\cos \dfrac {\pi }{4}=\dfrac {\sqrt {2}}{2}+\dfrac {\sqrt {2}}{2}=\sqrt {2}$
