\tan 75^\circ = \frac{1 + \frac1{\sqrt3}}{1 - 1 \cdot \frac1{\sqrt3}} = \frac{\frac{\sqrt3 + 1}{\sqrt3}}{\frac{\sqrt3 - 1}{\sqrt3}} = \frac{\sqrt3 + 1}{\sqrt3 - 1}. - Get link 4share