tan x = 1, tangent is positive in first and third quadrant. Hence the tan x will be 1 for x = pi/4 ans pi + pi/4 = 5pi/4
Your query was as to how does tanx = 1 lead to x = pi/4 and 5pi/4
The reason for the same has been explained. tan pi/4 = 1 as well as tan 5pi/4 = 1 therefore x = pi/4 and 5pi/4 between 0 to 2pi. I hope now it is clear.
Tangent is a periodic function with period . If, for some x and y, tan(x)= y then it is also true that for any integer, n. In particular, so . It is also true that , that , and that, in general, for any integer, n.