4) 5 sin(π/4) + 3 tg(π/4) − 5 cos(π/4) − 10 ctg(π/6).

Используем значения \(\sin(\pi/4)=\cos(\pi/4)=\frac{\sqrt2}{2}\), \( g(\pi/4)=1\), \(\ctg(\pi/6)=\sqrt3\).

\[5\cdot\frac{\sqrt2}{2}+3-5\cdot\frac{\sqrt2}{2}-10\sqrt3=3-10\sqrt3.\]

Ответ: \(3-10\sqrt3\).