Answer:
Only the second equation is an identity
Step-by-step explanation:
[tex]$8 \frac{\tan^2(\theta)}{\sec(\theta)} \csc^2(\theta)=8 \csc(\theta)$[/tex]
Note that
[tex]\tan^2(\theta)\csc^2(\theta)=\sec^2(\theta)[/tex]
You can confirm it:
[tex]$\frac{\sin^2(\theta)}{\cos^2(\theta)}\cdot \frac{1}{\sin^2(\theta)}= \frac{1}{cos^2(\theta)}= \sec^2(\theta)$[/tex]
Therefore
[tex]$8 \frac{\sec^2(\theta)}{\sec(\theta)} =8 \csc(\theta)$[/tex]
[tex]$8 \frac{\sec(\theta)}{1} =8 \csc(\theta)$[/tex]
[tex]8\sec(\theta)=8\csc(\theta)[/tex]
It is not an Identity
Let's the second one
[tex]$13 \frac{\tan^2(\theta)}{\sec(\theta)} \csc^2(\theta)=13\sec(\theta)$[/tex]
In this case, we already performed the calculations, so it is true. It is an Identity.
