Cos15+sin15=a/4cos15 a=?

[latex]cos15+sin15=cos15+cos75=2cos45\cdot cos30=\\\\=2\cdot \frac{\sqrt2}{2}\cdot \frac{\sqrt3}{2}=\frac{\sqrt6}{2}\\\\cos15=cos(45-30)=cos45\cdot cos30+sin45\cdot sin30=\\\\=\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{2}+\frac{\sqrt2}{2}\cdot \frac{1}{2}= \frac{\sqrt6+\sqrt2}{4} \\\\4cos15=\sqrt6+\sqrt2\\\\\\cos15+sin15=\frac{a}{4cos15}\; \; \to \\\\\frac{\sqrt6}{2}=\frac{a}{\sqrt6+\sqrt2}\\\\a= \frac{\sqrt6(\sqrt6+\sqrt2)}{2} = \frac{6+\sqrt{12}}{2} = \frac{6+2\sqrt3}{2} =3+\sqrt3[/latex]