How to simplify trig equations

express as a single trig ratio.

tan²x - sin²x / tan²xsin²x

I am assuming that the expression is:

[tan²(x) - sin²(x)]/[tan²(x)sin²(x)]

We can divide each term in the numerator by tan²(x)sin²(x) to get:

tan²(x)/[tan²(x)sin²(x)] - sin²(x)/[tan²(x)sin²(x)]
= 1/sin²(x) - 1/tan²(x)
= csc²(x) - cot²(x)

Therefore, since csc²(x) - cot²(x) is the Pythagorean identity, we can show that:

[tan²(x) - sin²(x)]/[tan²(x)sin²(x)] = 1

I hope this helps!