1. Basic trig

Need to find all solutions of this

$Tan^2 x = 1$

Book says ${\pi\over 4} + {\pi\over 2}N$

But its $Tan x = 1$ and $Tan x = -1$

So shouldnt the reference angle ( $\pi\over 4$) be in every quadrant?

2. 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 $\pi$ ) the solutions for one revolution of the unit circle will be

$x= \frac{\pi}{4},\frac{\pi}{2}+\frac{\pi}{4}$

All solutions are found then by mulitplying through these soultions into every other revolution of the circle.

So $x= \frac{(2k+1)\pi}{4},k=0,1,2,\dots$