If $$\cot x=\frac{5}{12}$$ for some $$x\in \left(\pi,\frac{3\pi}{2}\right)$$, then $$\sin 7x \left(\cos \frac{13x}{2}+\sin \frac{13x}{2}\right)+\cos 7x\left(\cos \frac{13x}{2}-\sin \frac{13x}{2}\right)$$ is equal to

A

$$\frac{5}{\sqrt{13}}$$

B

$$\frac{4}{\sqrt{26}}$$

C

$$\frac{6}{\sqrt{26}}$$

D

$$\frac{1}{\sqrt{13}}$$