Question

How do you prove that `(sinx-cosx-1)/(sinx+cosx-1)=(cosx+1)/sinx`?

Answer 1

Perhaps there was a mistype in this question:

Here is the graph of `(sinx-cosx-1)/(sinx+cosx-1)`:

graph{(sinx-cosx-1)/(sinx+cosx-1) [-10, 10, -5, 5]}

Here is the graph of `(cosx+1)/sinx`

graph{(cosx+1)/sinx [-10, 10, -5, 5]}:

It's flipped around, meaning the identity is false: one side of the equation is the negative of the other. If there was a negative sign on one side of them, then we could probably prove it.