Are these two answers correct? Please help, thanks! Julia wants to simplify the term in a trigonometric identity that she is proving. Which of the following identities should she use to help her? Select all that apply.

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.