Obliczmy bez użycia tablic matematycznych wartość cos15^o:

$\cos {30}^{\circ }=2{\cos }^2{15}^{\circ }-1$  

$\frac{\sqrt{3}}{2}=2{\cos }^2{15}^{\circ }-1$  

$2{\cos }^2{15}^{\circ }=\frac{\sqrt{3}}{2}+1$  

${\cos }^2{15}^{\circ }=\frac{\sqrt{3}}{4}+\frac{1}{2}$  

${\cos }^2{15}^{\circ }=\frac{\sqrt{3}}{4}+\frac{2}{4}$  

Zatem:

$\cos {15}^{\circ }=\sqrt{\frac{\sqrt{3}+2}{4}}=\frac{\sqrt{\sqrt{3}+2}}{2}\cdot \frac{2}{2}=\frac{\sqrt{4\sqrt{3}+8}}{4}=$  

$=\frac{\sqrt{6+2\cdot 2\sqrt{3}+2}}{4}=\frac{\sqrt{{\sqrt{6}}^2+2\cdot \sqrt{12}+{\sqrt{2}}^2}}{4}=$  

$=\frac{{\sqrt{\left(\sqrt{6}+\sqrt{2}\right)}}^2}{4}=\frac{\sqrt{6}+\sqrt{2}}{4}$