a)
[tex](cos120^o - ctg150^o)^2= (cos(90^o+30^o) - ctg(90^o+60^o))^2= (-sin30^o - \\ (-tg60^o))^2= (-\frac{1}{2} +\sqrt{3})^2= \frac{1}{4} -\sqrt{3} + 3 = 3\frac{1}{4} -\sqrt{3}[/tex]
b)
[tex]cos300^o : sin315^o = cos(360^o - 60^o):sin(360^o - 45^o) = cos60^o : (- sin45^o) = \\ = \frac{1}{2} : (- \frac{\sqrt{2}}{2}) =\frac{1}{\not{2}_1} \cdot (- \frac{\not{2}^1}{\sqrt{2}})= -\frac{1}{\sqrt{2}} =-\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}[/tex]
c)
[tex](sin135^o + tg120^o)^2 = (sin(90^o+45^o) + tg(90^o+30^o))^2 = (cos45^o+ \\ + (-ctg30^o))^2= (\frac{\sqrt{2}}{2} -\sqrt{3})^2= \frac{2}{4} - \sqrt{2} \cdot \sqrt{3}+3 =\frac{1}{2} - \sqrt{2 \cdot 3}+3 =3\frac{1}{2} -\sqrt{6}[/tex]
