1. Complex numbers
$$
\begin{array}{l}
z_{1}=\frac{1}{1+\cos \theta+i \sin \theta}+\frac{1}{1+\cos \theta-i \sin \theta}, \\
z_{2}=\frac{\cos \theta+i \sin \theta}{1+\cos \theta+i \sin \theta}+\frac{\cos \theta-i \sin \theta}{1+\cos \theta-i \sin \theta}
\end{array}
$$

The relationship between them is ().
(A) $z_{1}>z_{2}$
(B) $z_{1}=z_{2}$
(C) $z_{1}<z_{2}$
(D) Cannot compare the size
-1. (B).
Let $z=\cos \theta+i \sin \theta$, then $z \bar{z}=1$. We have
$$
\begin{array}{l}
z_{1}=\frac{z \bar{z}}{z \bar{z}+z}+\frac{1}{1+\bar{z}}=\frac{\bar{z}}{1+\bar{z}}+\frac{1}{1+\bar{z}}=1, \\
z_{2}=\frac{z}{z \bar{z}+z}+\frac{\bar{z}}{1+\bar{z}}=\frac{1}{1+\bar{z}}+\frac{\bar{z}}{1+\bar{z}}=1 .
\end{array}
$$

Therefore, $z_{1}=z_{2}=1$.