Ответ:

Используем формулу сложения косинусов: \(\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta\).

  1. \(\cos135^\circ=\cos(90^\circ+45^\circ)=0\cdot\frac{\sqrt2}{2}-1\cdot\frac{\sqrt2}{2}=-\frac{\sqrt2}{2}\).
  2. \(\cos120^\circ=\cos(90^\circ+30^\circ)=0\cdot\frac{\sqrt3}{2}-1\cdot\frac12=-\frac12\).
  3. \(\cos150^\circ=\cos(90^\circ+60^\circ)=0\cdot\frac12-1\cdot\frac{\sqrt3}{2}=-\frac{\sqrt3}{2}\).
  4. \(\cos240^\circ=\cos(180^\circ+60^\circ)=(-1)\cdot\frac12-0\cdot\frac{\sqrt3}{2}=-\frac12\).

Ответ: 1) \(-\frac{\sqrt2}{2}\); 2) \(-\frac12\); 3) \(-\frac{\sqrt3}{2}\); 4) \(-\frac12\).