trigonometry1 Questions and Answers

Start Your Free Trial

Solve equation tan^2x-8tanx+12=0

Expert Answers info

Tushar Chandra eNotes educator | Certified Educator

calendarEducator since 2010

write12,551 answers

starTop subjects are Math, Science, and Business

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

check Approved by eNotes Editorial

Related Questions

More »


Student Answers

giorgiana1976 | Student

To calculate the equation, it's proper to make th substitution tanx=t

(t)^2 - 8*t + 12 = 0

We'll apply quadratic formula

t1= [-(-8)+sqrt(64-48)]/2

t1=(8+4)/2

t1=6

tan x=t1

tan x=6

x = arctan 6 + k*pi

t2= (8-4)/2

t2= 2

tan x = 2

x = arctan 2 + k*pi

The solutions of the equation are {arctan 6 + k*pi}U{arctan 2 + k*pi}.

Ask a Question

Popular Questions

More »