A circle centered at O has radius 1 and contains point ,A Segment AB is tangent to the circle at A and $\angle$AOB = $\theta$
If point C lies on OA, and BC bisects the angle ABO, then OC equals

• A

  $\sec \mathrm{\theta }(\sec \mathrm{\theta }-\tan \mathrm{\theta })$

• B

  $\frac{{\cos }^2\mathrm{\theta }}{1+\sin \mathrm{\theta }}$

• C

  $\frac{1}{1+\sin \mathrm{\theta }}$

• D

  $\frac{1-\sin \mathrm{\theta }}{{\cos }^2\mathrm{\theta }}$