Question

Prove that `sec^2x/(sec^2x-1)=csc^2x`?

Answer 1

Please see below.

Explanation:

`sec^2x/(sec^2x-1)`

= `sec^2x/tan^2x`

= `(1/cos^2x)/(sin^2x/cos^2x)`

= `1/cos^2x xx cos^2x/sin^2x`

= `1/cancel(cos^2x) xx cancel(cos^2x)/sin^2x`

= `1/sin^2x`

= `csc^2x`