A circle centered at O has radius 1 and contains the point A. Segment A B is tangent to the circle at A and \angle A O B=\theta. If point C lies on \overline{O A} and \overline{B C} bisects \angle A B O, then O C=

**Answer Choices**

A. \sec ^{2} \theta-\tan \theta

B. \dfrac{1}{2}

C. \dfrac{\cos ^{2} \theta}{1+\sin \theta}

D. \dfrac{1}{1+\sin \theta}

E. \dfrac{\sin \theta}{\cos ^{2} \theta}