If $630°<A<720°$ and $\left|\tan A\right|=\frac{12}{5}$ then $\tan \frac{A}{2}=$

$\Rightarrow 630°<A<720°i.eA\in Q_4$

$\tan A=-\frac{12}{5}$

$\tan A=\frac{2\tan \frac{A}{2}}{1-{\tan }^2\frac{A}{2}}$

$\Rightarrow -\frac{12}{5}=\frac{2x}{1-x^2}\left[\tan \frac{A}{2}=x\right]$

$\Rightarrow -12+12x^2=10x$

$\Rightarrow 12x^2-10x-12=0$

$\Rightarrow 6x^2-5x-6=0$

$\Rightarrow 6x^2-9x+4x-6=0$

$\Rightarrow 3x\left[2x-3\right]+2\left[2x-3\right]=0$

$\Rightarrow \left[3x+2\right]\left[2x-3\right]=0$

$\Rightarrow x=-\frac{2}{3},x=\frac{3}{2}$

$\Rightarrow \tan \frac{A}{2}=-\frac{2}{3}$

$\because 315<\frac{A}{2}<360$