Let's help Julia to solve this problem. Given the term:
[tex]\frac{sec^{2}( \theta)-1}{cot^{2}( \theta)+1}[/tex]
We need to simplify it. So, we will take a look at the identities above, thus, from the second identity:
[tex]sec^{2}( \theta)-tan^{2}(\theta) = 1[/tex]
∴ [tex]sec^{2}( \theta)-1=tan^{2}(\theta)[/tex]
And from the five equation:
[tex]1 = csc^{2}( \theta)-cot^{2}(\theta)[/tex]
∴ [tex]cot^{2}(\theta)+1= csc^{2}( \theta)[/tex]
Substituting these identities in the term:
[tex]\frac{tan^{2}( \theta)}{csc^{2}( \theta)} = sin^{2}( \theta)tan^{2}( \theta)[/tex]
In fact, your answer is correct.
