13. (2 sin(π/4) + 3 cos(π/6)) / ctg(π/3)

Подставим значения: \(\sin\frac{\pi}{4}=\frac{\sqrt2}{2}\), \(\cos\frac{\pi}{6}=\frac{\sqrt3}{2}\), \(\ctg\frac{\pi}{3}=\frac{1}{\sqrt3}\).

\(\frac{2\cdot\frac{\sqrt2}{2}+3\cdot\frac{\sqrt3}{2}}{\frac{1}{\sqrt3}}=\left(\sqrt2+\frac{3\sqrt3}{2}\right)\sqrt3=\sqrt6+\frac92.\)

Ответ: \(\sqrt6+\frac92\).