Need help solving trigonometry problem

Question

Here is the equation: 4+tan^2(x)-sec^2(x)/csc^2(x)

I need to simplify it so it equals to 3sin^2(x)

The question is 5D. The steps are very confusing for me so I would appreciate it if someone could simplify them.

Here is the link: https://www.engageny.org/sites/default/files/downloadable-resources/2014/Sep/algebra-ii-m2-topic-b-lesson-16-teacher.pdf

Answer 1

secx = 1/cosx

cscx = 1/sinx

secx/cscx = (1/cosx)/(1/sinx) = sinx/cosx = tanx

sec²x/csc² = tan²x = sin²x/cos²x

4 + tan²x - tan²x = 4 the squared terms cancel out, the 2nd and 3rd terms cancel

The 3 terms sum to 4, not 3sin²x

Your answer key has a mistake or the problem has a typo somewhere

Look at a table of trig identities. It might help.

A common way to work some of these problems is convert everything or some things to sines & cosines and you see the relations better.