
Basic trig
Need to find all solutions of this
$\displaystyle Tan^2 x = 1$
Book says $\displaystyle {\pi\over 4} + {\pi\over 2}N$
But its $\displaystyle Tan x = 1$ and $\displaystyle Tan x = 1$
So shouldnt the reference angle ($\displaystyle \pi\over 4$) be in every quadrant?

The question implies you need to find what angles will give a positive solution for x. Only the 1st and 3rd quadrants have a positive answer for x so you need to find these.
Using the symmerty identities (keeping in mind that tan has the preiod of $\displaystyle \pi$ ) the solutions for one revolution of the unit circle will be
$\displaystyle x= \frac{\pi}{4},\frac{\pi}{2}+\frac{\pi}{4}$
All solutions are found then by mulitplying through these soultions into every other revolution of the circle.
So $\displaystyle x= \frac{(2k+1)\pi}{4},k=0,1,2,\dots$