[tex]a) \frac{sin120+cos135}{2tg150}=\frac{sin(90+30)+cos(90+45)}{2tg(180-30)}=\frac{cos30+(-sin45)}{2(-tg30)}=\frac{\frac{\sqrt3}{2}+(-\frac{\sqrt2}2)}{2*(-\frac{\sqrt3}3)}=\frac{\frac{\sqrt3-\sqrt2}{2}}{-\frac{2\sqrt3}3}=\frac{\sqrt3-\sqrt2}2*(-\frac3{2\sqrt3})=-\frac{3(\sqrt3-\sqrt2)}{4\sqrt3}=-\frac{3\sqrt3(\sqrt3-\sqrt2)}{4*3}=-\frac{\sqrt3(\sqrt3-\sqrt2)}4=-\frac{3-\sqrt6}4=\frac{-3+\sqrt6}4[/tex]
[tex]b)\\\\\frac{sin^2135+sin^245}{cos45-cos135}=\frac{sin^2(90+45)+sin^245}{cos45-cos(90+45)}=\frac{cos^245+sin^245}{cos45-(-sin45)}=\frac{(\frac{\sqrt2}2)^2+(\frac{\sqrt2}2)^2}{\frac{\sqrt2}2-(-\frac{\sqrt2}2)}=\frac{\frac24+\frac24}{\frac{\sqrt2}2+\frac{\sqrt2}2}=\frac{1}{\sqrt2}=\frac{\sqrt2}2[/tex]
