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
We’ll help your grades soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support
Already a member? Log in here.
Are you a teacher? Sign up now