We have to solve the equation: (tan x)^2 - 8 tan x + 12 = 0
let tan x = y
(tan x)^2 - 8 tan x + 12 = 0
=> y^2 - 8y + 12 = 0
=> y^2 - 6y - 2y + 12 = 0
=>...
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We have to solve the equation: (tan x)^2 - 8 tan x + 12 = 0
let tan x = y
(tan x)^2 - 8 tan x + 12 = 0
=> y^2 - 8y + 12 = 0
=> y^2 - 6y - 2y + 12 = 0
=> y(y -6) - 2( y - 6) = 0
=> ( y - 2)(y - 6) = 0
So y = 2 and y = 6
As y = tan x
tan x = 2 and tan x = 6
=> x = arc tan 2 + n*pi and x = arc tan 6 + n*pi
Therefore the solution is
x = arc tan 2 + n*pi and
x = arc tan 6 + n*pi