If $\theta$ is real, the modulus of $\frac{1}{(1+\cos \theta) + i \sin \theta}$ is :

Question

( A ) $\sec \frac{\theta}{2}$
( B ) $\frac{1}{2} \cos \frac{\theta}{2}$
( C ) $\cos \frac{\theta}{2}$
( D ) $\frac{1}{2} \sec \frac{\theta}{2}$