The title is not exactly what I'm asking, so sorry for that.
I was doing a problem in my mathematics text book.
It is given that $|x|<a$, I thought if $a=2$ then we can put $x=1$ but what if when $a=-2$ then too we can put $x=1$ but then $|x| \not< a$.
When we have $x=1$ and $a=2$ then we will have same expression as when $x=1$ and $a=-2$(with negative sign) because ultimately we have $a^2=4$ in both the case.
The problem is that I don't believe that book is wrong but if book is correct then where I'm making mistake? Kindly clear my confusion.
What I have thought
If $a$ is negative then $|x|<a$ will have no solution.
Domain of function $\tan^{-1}$ is $\mathbb{R}$.