Question

How do you find the x intercepts for `y=sec^2x-1`?

Answer 1

`pi+pin=x`

Explanation:

Note that `sec^2x-1=tan^2x`. Hence, we can replace the original equation for a simpler one. Albeit working with `sec` is also easy in this case, it's a good habit to work with fewer terms. (There are occasions in which this is not true, but that will with experience.)

Also, note that the only way for `tan^2x=0` is when `tanx=0`.
So, when is it zero? If you remember the unit circle, you can see that `tanx=o/a`, where `o` is the opposite side in the unit circle, and `a` the adjacent.

Hence, you want `o=0`. And that happens when `pi+pin=x`, where `pi` is any integer.
Here's a graphical representation:
graph{tanx [-10, 10, -5, 5]}