From Förberedande kurs i matematik 1

If we draw the angle \displaystyle 225^{\circ} = 180^{\circ} + 45^{\circ} on a unit circle, we see that it makes an angle of \displaystyle 45^{\circ} with the negative x-axis.

This means that \displaystyle \tan 225^{\circ}, which is the slope of the line that makes an angle of \displaystyle 45^{\circ} with the positive x-axis, equals \displaystyle \tan 45^{\circ}, because the line which makes an angle of \displaystyle 45^{\circ} has the same slope,

\displaystyle \tan 225^{\circ} = \tan 45^{\circ} = \frac{\sin 45^{\circ}}{\cos 45^{\circ}} = \frac{\dfrac{1}{\sqrt{2}}}{\dfrac{1}{\sqrt{2}}} = 1\,\textrm{.}