Two functions are called cofunctions if they are equal on complementary angles
[tex]\csc \theta=\sec (\frac{\pi}{2}-\theta)[/tex]Since
[tex]\theta=\frac{\pi}{4}[/tex]Substitute it in the rule above
[tex]\csc (\frac{\pi}{4})=sec(\frac{\pi}{2}-\frac{\pi}{4})[/tex][tex]\csc (\frac{\pi}{4})=\sec (\frac{\pi}{4})[/tex]The cofunction is sec(pi/4)