If $$\frac{\pi}{2}\leq x\leq \frac{3\pi}{4}$$, then $$\cos^{-1}\left(\frac{12}{13}\cos x+\frac{5}{13}\sin x\right)$$ is equal to

A

$$x-\tan^{-1} \frac{4}{3}$$

B

$$x+\tan^{-1} \frac{4}{5}$$

C

$$x-\tan^{-1} \frac{5}{12}$$

D

$$x+\tan^{-1} \frac{5}{12}$$