Question

How do you simplify `(sin² t - cos² t sin² t) / sin² t`?

Answer 1

`sin^2t`

Explanation:

First off, I am lead to believe the "t" outside the denominator is a mistake. Secondly, for my convenience I changed "t" to "x".

1) Since in this equation the numerator has a subtraction we could and will split the numerator.
2) Now that the numerator is split we can simplify `sin^2t/sin^2t` into 1. As well as cancel `sin^2t` in both the numerator and denominator for the other fraction.
3) This leaves us with `1-cos^2t`, which if you notice is the Pythagorean Identity of `sin^2x+cos^2x=1`, but is can be rewritten as `sin^2x=1-cos^2x`. So now that we know it is an identity we can simplify it as `sin^2t`.