Answer:
See below.
Step-by-step explanation:
[tex]\frac{1+cos(\theta)}{sin(\theta)} +\frac{sin(\theta)}{1+cos(\theta)}=2csc(\theta)[/tex]
[tex]\frac{(1+cos(\theta))(1+cos(\theta))}{sin(\theta)((1+cos(\theta))} +\frac{(sin(\theta))(sin(\theta))}{(1+cos(\theta))(sin(\theta))}=2csc(\theta)[/tex]
[tex]\frac{(1+cos(\theta))(1+cos(\theta))+(sin(\theta))(sin(\theta))}{sin(\theta)((1+cos(\theta))}=2csc(\theta)[/tex]
[tex]\frac{(1+2cos(\theta)+cos^2(\theta)+sin^2(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]
Recall the identities:
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]
[tex]\frac{1+2cos(\theta)+1}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]
[tex]\frac{2+2cos(\theta)}{sin(\theta)(1+cos(\theta)}=2csc(\theta)[/tex]
[tex]\frac{2(1+cos(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]
[tex]\frac{2}{sin(\theta)} =2csc(\theta)[/tex]
[tex]2csc(\theta)=2csc(\theta)[/tex]
