Can someone explain me the steps to this 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

sec²x/csc²x = sin²x/cos²x = tan²x

tan²x = sin²x/cos²x

It all cancels, except for 4

4 + tan²x - sec²x/csc²x = 4 not 3sin²x

Maybe if you look at the more simple trig relations

tanx=sinx/cosx

secx = 1/cosx

cscx = 1/sinx

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

now square them and secx²/csc²x = tan²x

2nd term is same as the 3rd term, they subtract, leaving only the first term, 4.

Unless you have a typo in the problems somewhere. The way it's written the only answer is 4.