Chapter 7 - 7.1 - Using Fundamental Identities - 7.1 Exercises - Page 513: 43

$\frac{1}{1+cos~x}+\frac{1}{1-cos~x}=2~csc~x$

$\frac{1}{1+cos~x}+\frac{1}{1-cos~x}=\frac{1(1-cos~x)}{(1+cos~x)(1-cos~x)}+\frac{1(1+cos~x)}{(1-cos~x)(1+cos~x)}=\frac{1-cos~x}{1-cos^2~x}+\frac{1+cos~x}{1-cos^2~x}=\frac{2}{1-cos^2~x}=\frac{2}{sin^2x}=2~csc~x$