we know that
the angle (pi/4)---------> is equal to 180°/4-----> 45°
45° belong to the I quadrant
so
sin 45° is positive--------> √2/2
cos 45° is positive-------> √2/2
tan 45° is positive-------> 1
the angle (5pi/4)---------> is equal to 5*180°/4-----> 225°
225° belong to the III quadrant
so
sin 225° is negative -------> -√2/2
cos 225° is negative-------> -√2/2
tan 225° is positive-------> 1
therefore
tan(5*pi*/4) and tan(pi/4) -------> they have the same value