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

=\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\times \frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}=22×32+22×12=6+24

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

=\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}\times \frac{1}{2}=\frac{\sqrt{6}-\sqrt{2}}{4}=22×32−22×12=6−24

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

=\frac{1-\frac{\sqrt{3}}{3}}{1+\frac{\sqrt{3}}{3}}=2-\sqrt{3}=1−331+33=2−3