cos15^{\circ}=cos(45^{\circ}-30^{\circ})=cos45^{\circ}cos30^{\circ}+sin45^{\circ}sin30^{\circ}

=\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\times \frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}

sin15^{\circ}=sin(45^{\circ}-30^{\circ})=sin45^{\circ}cos30^{\circ}-cos45^{\circ}sin30^{\circ}

=\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}\times \frac{1}{2}=\frac{\sqrt{6}-\sqrt{2}}{4}

tan15^{\circ}=tan(45^{\circ}-30^{\circ})=\frac{tan45^{\circ}-tan30^{\circ}}{1+tan45^{\circ}tan30^{\circ}}

=\frac{1-\frac{\sqrt{3}}{3}}{1+\frac{\sqrt{3}}{3}}=2-\sqrt{3}