Remember that
[tex]\cos (\frac{x}{2})=\pm\sqrt[]{\frac{1_{}+\cos x}{2}}[/tex]For x=30 degrees
[tex]\cos (\frac{30^o}{2})=\cos (15^o)=\sqrt[]{\frac{1+\cos 30^o}{2}}[/tex]we know that
[tex]\cos 30^o=\frac{\sqrt[]{3}}{2}[/tex]substitute
[tex]\cos (15^o)=\sqrt[]{\frac{1+\frac{\sqrt[]{3}}{2}}{2}}[/tex][tex]\cos (15^o)=\sqrt[]{\frac{2+\sqrt[]{3}}{4}}[/tex][tex]\cos (15^o)=\frac{\sqrt[]{2+\sqrt[]{3}}}{2}[/tex]