Answer
$\dfrac {\sqrt {2}}{2}\left( \cos \theta +\sin \theta \right) $
Work Step by Step
$\sin \left( 45+\theta \right) =\sin 45\cos \theta +\cos 45\sin \theta =\dfrac {\sqrt {2}}{2}\cos \theta +\dfrac {\sqrt {2}}{2}\sin \theta =\dfrac {\sqrt {2}}{2}\left( \cos \theta +\sin \theta \right) $
