$$\lim_{x \to \frac{\pi}{2}} {\tan^2 x(2\sin^2 x + 3\sin x + 4)^{\frac{1}{2}} - (\sin^2 x + 6\sin x + 2)^{\frac{1}{2}}}{2}$$ is equal to

A

$$\frac{1}{12}$$

B

$$-\frac{1}{18}$$

C

$$-\frac{1}{12}$$

D

$$\frac{1}{6}$$