If \( \cos (\theta-\alpha), \cos \theta \) and \( \cos (\theta+\alpha) \) are in H.P., then \( \...

If \( \cos (\theta-\alpha), \cos \theta \) and \( \cos (\theta+\alpha) \) are in H.P., then \( \cos \theta \sec \frac{\alpha}{2} \) is equal to
(A) \( \pm \sqrt{2} \)
(B) \( \pm \sqrt{3} \)
(C) \( \pm 1 / \sqrt{2} \)
(D) None of these