1. Вычислите: а) −9√6 cos(5π/3) · sin(5π/4); б) sin 5π + 4 cos(14π/3) + tg(−25π/4); в) (ctg(9π/4) + tg(8π/3))(sin(9π/2) − 2 cos(7π/6)).

а) Используем значения тригонометрических функций: \(\cos\frac{5\pi}{3}=\frac12\), \(\sin\frac{5\pi}{4}=-\frac{\sqrt2}{2}\).

\(-9\sqrt6\cdot\frac12\cdot\left(-\frac{\sqrt2}{2}\right)=\frac{9\sqrt{12}}4=\frac{9\sqrt3}2\).

б) \(\sin 5\pi=0\), \(\cos\frac{14\pi}{3}=\cos\frac{2\pi}{3}=-\frac12\), \( g\left(-\frac{25\pi}{4}\right)= g\left(-\frac\pi4\right)=-1\) (период тангенса равен \(\pi\)).

\(0+4\cdot\left(-\frac12\right)-1=-3\).

в) \(\ctg\frac{9\pi}{4}=1\), \( g\frac{8\pi}{3}=-\sqrt3\), \(\sin\frac{9\pi}{2}=1\), \(\cos\frac{7\pi}{6}=-\frac{\sqrt3}{2}\).

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

Ответ: а) \(\frac{9\sqrt3}{2}\); б) \(-3\); в) \(-2\).