[tex]\displaystyle cos(a\pm b)=cosacosb\mp sinasinb \\ \\ cos75=cos(45+30)=cos45cos30-sin45sin30= \\ \\ =\frac{\sqrt2}{2}\frac{\sqrt3}{2}-\frac{1}{2}\frac{\sqrt2}{2}= \\ \\ =\frac{\sqrt6-\sqrt{2}}{4} \\ \\ cos15=cos(45-30)=cos45cos30+sin45sin30= \\ \\ =\frac{\sqrt2}{2}\frac{\sqrt3}{2}+\frac{\sqrt2}{2}\frac{1}{2}= \\ \\ =\frac{\sqrt2+\sqrt6}{4} \\ \\ cos15+cos75=\frac{\sqrt2+\sqrt6}{4}+\frac{\sqrt6-\sqrt2}{4}=\frac{\sqrt6}{2}[/tex]
