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\(\cfrac{tan60° – tan30°}{1+tan60° tan30°} + cos60°cos30° \)\(+ sin60°sin30°\)
\(=\cfrac{\sqrt3–\cfrac{1}{\sqrt3}}{1+\sqrt3.\cfrac{1}{\sqrt3}} + \cfrac{1}{2}.\cfrac{\sqrt3}{2} \)\(+ \cfrac{\sqrt3}{2}.\cfrac{1}{2}\)
\(=\cfrac{\cfrac{3-1}{\sqrt3}}{1+1} +\cfrac{\sqrt3}{4} \)\(+ \cfrac{\sqrt3}{4}\)
\(=\cfrac{\cfrac{2}{\sqrt3}}{2} +\cfrac{\sqrt3}{4} \)\(+ \cfrac{\sqrt3}{4}\)
\(=\cfrac{1}{\sqrt3} +\cfrac{\sqrt3}{4} \)\(+ \cfrac{\sqrt3}{4}\)
\(=\cfrac{4+3+3}{4\sqrt3} \)
\(=\cfrac{10\times \sqrt3}{4\sqrt3 \times \sqrt3} \)
\(=\cfrac{10 \sqrt3}{12} \)
\(=\cfrac{5 \sqrt3}{6} \)