In $\triangle A B C$, if $A=\frac{\pi}{3}$ and $B=\frac{\pi}{4}$, then $\frac{a^2-b^2}{c^2}=$

In a $\triangle A B C$, if $a=3, b=7$ and $c=8$, then $\sin \frac{B}{2} \tan \frac{C-A}{2}=$

In a $\triangle A B C, A D$ and $B E$ are medians. If $A D=4, \angle D A B=\frac{\pi}{6}$ and $\angle A B E=\frac{\pi}{3}$, then the area of $\triangle A B C$ is

If $S$ is the circumentre of a $\triangle A B C, a=5, b=6, c=9$ and $S B=\frac{27}{4 \sqrt{2}}$, then $\sin 2 C=$