Question

How do you prove that `sec^2x+csc^2x=1` is not an identity?

Answer 1

`sec^2x+csc^2x=1/(sin^2xcos^2x)`

Explanation:

Since `secx=1/cosx` and `cscx=1/sinx`, you will get:

`sec^2x+csc^2x=1/cos^2x+1/sin^2x`

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

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