Question

How do you simplify `sin^2x csc^2x - sin^2x`?

Answer 1

The expression simplifies into `cos^2(x)`

Explanation:

You only need to write down the definitions: since `csc(x)=1/{\sin(x)}`, we have that

`\sin^2(x) * csc^2(x) - \sin^2(x) = {\sin^2(x)}/{\sin^2(x)} - \sin^2(x)`

The first term is obviously `1`, so you have `1-\sin^2(x)`, which equals `\cos^2(x)` because of the fundamental formula `\cos^2(x)+\sin^2(x)=1`