Precalc Trig

tan^2 (x)  - 1  = 0     factor this as a difference of squares

[ tan x  - 1 ]  [ tan x  +  1  ]   = 0

Set each factor to 0   and solve for x

tan x  -  1   =   0      add 1 to both sides

tan x   =   1         and this occurs at    pi/4 +  pi*n   where n is an integer

And

tan x  +  1  = 0      subtract 1 from both sides

tan x  =  - 1      and this occurs at  (3pi)/4   +  pi*n    where n is an integer