Question

Are these two answers correct? Please help, thanks!

Answer 1

Let's help Julia to solve this problem. Given the term:

$\frac{sec^{2}( \theta)-1}{cot^{2}( \theta)+1}$

We need to simplify it. So, we will take a look at the identities above, thus, from the second identity:

$sec^{2}( \theta)-tan^{2}(\theta) = 1$

∴ $sec^{2}( \theta)-1=tan^{2}(\theta)$

And from the five equation:

$1 = csc^{2}( \theta)-cot^{2}(\theta)$

∴ $cot^{2}(\theta)+1= csc^{2}( \theta)$

Substituting these identities in the term:

$\frac{tan^{2}( \theta)}{csc^{2}( \theta)} = sin^{2}( \theta)tan^{2}( \theta)$

In fact, your answer is correct.

Answer 2

Let's help Julia to solve this problem. Given the term:

We need to simplify it. So, we will take a look at the identities above, thus, from the second identity:

∴

And from the five equation:

∴

Substituting these identities in the term:

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