Answer
$${\text{sec}}\left( {\frac{\pi }{2} - \theta } \right) = \csc \theta $$
Work Step by Step
$$\eqalign{
& {\text{Let }}y = {\text{sec}}\left( {\frac{\pi }{2} - \theta } \right) \cr
& {\text{Use the identity }}\sec \alpha = \frac{1}{{\cos \alpha }},{\text{ then}} \cr
& y = \frac{1}{{\cos \left( {\frac{\pi }{2} - \theta } \right)}} \cr
& {\text{Where cos}}\left( {A - B} \right) = \cos A\cos B + \sin A\sin B \cr
& y = \frac{1}{{\cos \left( {\frac{\pi }{2}} \right)\cos \left( \theta \right) + \sin \left( {\frac{\pi }{2}} \right)\sin \left( \theta \right)}} \cr
& {\text{Simplify}} \cr
& y = \frac{1}{{\left( 0 \right)\cos \left( \theta \right) + 1 \sin \left( \theta \right)}} \cr
& y = \frac{1}{{\sin \theta }} \cr
& y = \csc \theta \cr
& {\text{Therefore,}} \cr
& {\text{sec}}\left( {\frac{\pi }{2} - \theta } \right) = \csc \theta \cr} $$
