If $\tanh x=\frac{1}{2}$, then $\sinh 2 x-\operatorname{sech} 2 x=$

If $A$ and $B(A>B)$ are acute angles, $\sin (A-B)=\frac{16}{65}$ and $\sin B=\frac{5}{13}$, then $\tan A+\cot A=$

If $\tan A=\frac{2}{3}$, then $\sin 4 A=$

$$ \frac{\sqrt{2} \cos 45^{\circ}+\cos 56^{\circ}+\cos 58^{\circ}-\cos 66^{\circ}}{\sqrt{2} \cos 28^{\circ} \cos 29^{\circ} \sin 33^{\circ}} $$