Suppose $$\theta$$ and $$\phi(\neq 0)$$ are such that $$\sec(\theta + \phi)$$, $$\sec\theta$$ and $$\sec(\theta - \phi)$$ are in A.P. If $$\cos\theta = k\cos\left(\frac{\phi}{2}\right)$$ for some $$k$$, then $$k$$ is equal to

A

$$\pm\sqrt{2}$$

B

$$\pm 1$$

C

$$\pm\frac{1}{\sqrt{2}}$$

D

$$\pm 2$$