Zadanie 4
a)
{sin225^{\circ} \cdot ctg 495^{\circ}=sin(225^{\circ}+45^{\circ})\cdot ctg(360^{\circ}+135^{\circ})=-sin45^{\circ}\cdot ctg135^{\circ}=}
{=-sin45^{\circ}\cdot ctg(180^{\circ}-45^{\circ})=-sin45^{\circ}\cdot (-ctg45^{\circ})=(-\frac{\sqrt2}{2})\cdot (-1)=\frac{\sqrt2}{2}}
b)
{cos(-570^{\circ}) * tg(-1230^{\circ})=-cos(3\cdot 180^{\circ}+30^{\circ})\cdot [-tg(3\cdot 360^{\circ}+150^{\circ})]=-cos30^{\circ}\cdot (-tg150^{\circ})=}
{-cos30^{\circ}\cdot [-tg(90^{\circ}+60^{\circ})]=-cos30^{\circ}\cdot [-(-ctg60^{\circ})]=-\frac{\sqrt3}{2}\cdot \frac{\sqrt3}{3}=-\frac{3}{6}=-\frac{1}{2}}