$\text{a})$  

$\cos {75}^{\circ }=\cos \left({45}^{\circ }+{30}^{\circ }\right)=\cos {30}^{\circ }\cdot \cos {45}^{\circ }-\sin {30}^{\circ }\cdot \sin {45}^{\circ }=$

$=\frac{\sqrt{6}}{4}-\frac{\sqrt{2}}{2}=\frac{\sqrt{6}-\sqrt{2}}{4}$ $=\frac{\sqrt{6}}{4}-\frac{\sqrt{2}}{2}=\frac{\sqrt{6}-\sqrt{2}}{4}$

 

$\text{b})$

$\sin {105}^{\circ }=\sin \left({60}^{\circ }+{45}^{\circ }\right)=$   $\sin {60}^{\circ }\cos {45}^{\circ }+$

$=\frac{\sqrt{6}+\sqrt{2}}{4}$

 

$\text{c})$

$\cos \left(\frac{\pi }{12}\right)=\cos {15}^{\circ }=\cos \left({45}^{\circ }-{30}^{\circ }\right)=$

$=\cos {45}^{\circ }\cos {30}^{\circ }$

$=\frac{\sqrt{6}+\sqrt{2}}{4}$