$A=(\sin 20^{\circ}+\sin 70^{\circ})^{2}+(\cos 20^{\circ}+\cos 110^{\circ})^{2}$
$=(\cos 70^{\circ}+\cos 20^{\circ})^{2}+(\cos 20^{\circ}+\cos 110^{\circ})^{2}$
$=(-\cos 110^{\circ}+\cos 20^{\circ})^{2}+(\cos 20^{\circ}+\cos 110^{\circ})^{2}$
$=2((cos 20^{\circ})^{2}+(cos 110^{\circ})^{2})$
$=2((sin 70^{\circ})^{2}+(-cos 70^{\circ})^{2})$
$=2$
$B=\tan 20^{\circ}+\cot 20^{\circ}+\tan 110^{\circ}+\cot 110^{\circ}$
$=\cot 70^{\circ}+\tan 70^{\circ}-\tan 70^{\circ}-\cot 70^{\circ}$
$=0$