若 $\alpha \in\left(\frac{\pi}{4}, \frac{3 \pi}{4}\right), 6 \tan \left(\frac{\pi}{4}+\alpha\right)+4 \cos \left(\frac{\pi}{4}-\alpha\right)=5 \cos 2 \alpha$, 则 $\sin 2 \alpha=$
$\text{A.}$ $\frac{24}{25}$
$\text{B.}$ $\frac{12}{25}$
$\text{C.}$ $\frac{7}{25}$
$\text{D.}$ $\frac{1}{5}$