Answer
$\dfrac {\sqrt {2}}{2}\left( \cos x+\sin x\right) $
Work Step by Step
$\sin \left( \dfrac {\pi }{4}+x\right) =\sin \dfrac {\pi }{4}\cos x+\cos \dfrac {\pi }{4}\sin x=\dfrac {\sqrt {2}}{2}\cos x+\dfrac {\sqrt {2}}{2}\sin x=\dfrac {\sqrt {2}}{2}\left( \cos x+\sin x\right) $
