$\begin{align}  & \cos \left( \theta +\frac{\pi }{4} \right)=\cos \theta \cos \frac{\pi }{4}-\sin \theta \sin \frac{\pi }{4} \\ & \cos \left( \theta +\frac{\pi }{4} \right)=\frac{\sqrt{2}}{2}\cos \theta -\frac{\sqrt{2}}{2}\sin \theta  \\ & \cos \left( \theta +\frac{\pi }{4} \right)=\frac{\sqrt{2}}{2}\left( \cos \theta -\sin \theta  \right) \\\end{align}$