$\text{a)}2\sin {60}^{\text{o}}\cdot \cos {30}^{\text{o}}-2\text{tg}{45}^{\text{o}}={\sout{2}}^1\cdot \frac{\sqrt{3}}{{\sout{2}}^1}\cdot \frac{\sqrt{3}}{2}-2\cdot 1=\frac{3}{2}-2=-\frac{1}{2}$  
$\text{b)}\frac{{\sin }^2{45}^{\text{o}}+\cos {60}^{\text{o}}}{\sin {30}^{\text{o}}\cdot \cos {30}^{\text{o}}}=\frac{{\left(\frac{\sqrt{2}}{2}\right)}^2+\frac{1}{2}}{\frac{1}{2}\cdot \frac{\sqrt{3}}{2}}=\frac{\frac{2}{4}+\frac{1}{2}}{\frac{\sqrt{3}}{4}}=\frac{1}{\frac{\sqrt{3}}{4}}=\frac{4}{\sqrt{3}}=\frac{4\sqrt{3}}{3}$   

$\text{c)}{\left(\frac{\text{tg}{60}^{\text{o}}}{\cos {60}^{\text{o}}}-\frac{\sin {45}^{\text{o}}}{\cos {45}^{\text{o}}}\right)}^2={\left(\frac{\sqrt{3}}{\frac{1}{2}}-\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}\right)}^2={\left(2\sqrt{3}-1\right)}^2=12-4\sqrt{3}+1=13-4\sqrt{3}$  

$\text{d)}\frac{\sin {30}^{\text{o}}\cdot \text{tg}{60}^{\text{o}}+\cos {30}^{\text{o}}}{\text{tg}{30}^{\text{o}}}=\frac{\frac{1}{2}\cdot \sqrt{3}+\frac{\sqrt{3}}{2}}{\frac{\sqrt{3}}{3}}=\left(\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}\right)\cdot \frac{3}{\sqrt{3}}=\frac{{\sout{2}}^1{\sout{\sqrt{3}}}^1}{{\sout{2}}^1}\cdot \frac{3}{{\sout{\sqrt{3}}}^1}=3$