a) Ta có: \(\cos 52^{\circ}=\sin(90^o - 52^o)=\sin 38^{\circ}\);
          \(\cos 80^{\circ}=\sin (90^o - 80^o)=\sin 10^{\circ}.\)
          \(\cos 20^{\circ}=\sin (90^o - 20^o)=\sin 70^{\circ}.\)
Vì \( 10^o < 31^o < 38^o < 39^o <40^o <70^o\)  
\(\Rightarrow \sin 10^{\circ}<  \sin 31^{\circ}< \sin 38^{\circ}< \sin 39^{\circ}< \sin 40^{\circ}< \sin 70^{\circ}\) 
\(\Rightarrow  \cos 80^{\circ}< \sin 31^{\circ}< \cos 52^{\circ} < \sin 39^o< \sin 40^o< \cos 20^o\).
b) Ta có: \(\cot 72^{\circ}=\tan (90^o - 72^o)=\tan 18^{\circ}\)
          \(\cot 70^{\circ}=\tan (90^o - 70^o)=\tan 20^{\circ}\).
          \(\cot 50^{\circ}=\tan (90^o - 50^o)=\tan 40^{\circ}\)
Vì \(18^o < 20^o < 27^o < 37^o< 40^o< 52^o\)
\(\Rightarrow \tan 18^{\circ}< \tan 20^{\circ}< \tan 27^{\circ}< \tan 37^{\circ}< \tan 40^{\circ}< \tan 52^{\circ};
\\\Rightarrow \cot 72^{\circ}< \cot 70^{\circ}< \tan 27^{\circ}< \tan 37^{\circ}< \cot 50^{\circ}< \tan 52^{\circ}\).