Question

How do you use the fundamental identities to simplify `(1-sin^2x)/(csc^2x-1)`?

Answer 1

`(1-sin^2x)/(csc^2x-1)=sin^2x`

Explanation:

`(1-sin^2x)/(csc^2x-1)`

= `cos^2x/(1+cot^2x-1)`

= `cos^2x/cot^2x`

= `cos^2x/(cos^2x/sin^2x)`

= `cos^2x xx sin^2x/cos^2x`

= `sin^2x`