Answer
$$\frac{{\sqrt 2 }}{2}\left( {\cos \theta + \sin \theta } \right)$$
Work Step by Step
$$\eqalign{
& \cos \left( {{{45}^ \circ } - \theta } \right) \cr
& {\text{Use cosine difference identity}} \cr
& \cos \left( {{{45}^ \circ } - \theta } \right) = \cos \left( {{{45}^ \circ }} \right)\cos \left( \theta \right) + \sin \left( {{{45}^ \circ }} \right)\sin \left( \theta \right) \cr
& {\text{Simplify}} \cr
& \cos \left( {{{45}^ \circ } - \theta } \right) = \frac{{\sqrt 2 }}{2}\cos \left( \theta \right) + \frac{{\sqrt 2 }}{2}\sin \left( \theta \right) \cr
& \cos \left( {{{45}^ \circ } - \theta } \right) = \frac{{\sqrt 2 }}{2}\left( {\cos \theta + \sin \theta } \right) \cr} $$
