tan x +1 =2
Subtract 1 from each side
tan x +1-1 = 2-1
tan x = 1
Take the inverse tan of each side
tan^-1 (tan x) = tan^-1 (1)
x = pi/4 + pi * n where n is an integer
We are restricted on the interval from [0,2pi)
pi/4 + pi *0 and pi/4 + pi*1 ( if n is larger than 1 or smaller than 0 we go outside the interval)
pi/4 and pi/4 + 4pi/4
pi/4 and 5pi/4