Answer
$$\frac{{\sqrt 2 }}{2}$$
Work Step by Step
$$\eqalign{
& \cos \left( { - {{45}^ \circ }} \right) \cr
& {\text{use the identity cos}}\left( { - \theta } \right) = \cos \theta \cr
& = \cos \left( {{{45}^ \circ }} \right) \cr
& {\text{using the }}{45^ \circ }{\text{ - 4}}{{\text{5}}^ \circ }{\text{ - 9}}{{\text{0}}^ \circ }{\text{ triangle to obtain}} \cr
& \cos {45^ \circ } = \frac{{{\text{adjacent side to the 4}}{{\text{5}}^ \circ }}}{{{\text{hyppotenuse}}}} \cr
& {\text{then}} \cr
& \cos {45^ \circ } = \frac{1}{{\sqrt 2 }} \cr
& \cos {45^ \circ } = \frac{{\sqrt 2 }}{2} \cr
& or \cr
& \cos \left( { - {{45}^ \circ }} \right) = \frac{{\sqrt 2 }}{2} \cr} $$
