[tex] (cos30 \textdegree+sin30 \textdegree)(cos60 \textdegree-sin60 \textdegree)=(\frac{\sqrt3}{2}+\frac{1}{2})(\frac{1}{2}-\frac{\sqrt3}{2})=\frac{\sqrt3+1}{2}*\frac{1-\sqrt3}{2}=\frac{(\sqrt3+1)(1-\sqrt3)}{4}=\frac{\sqrt3-\sqrt3^2+1-\sqrt3}{4}=\frac{-3+1}{4}=\frac{-2}{4}=\frac{-1}{2} [/tex]
