Solve this equation: `tan^2 x - 3tan x + 2 = 0`

Expert Answers
embizze eNotes educator| Certified Educator

Solve `tan^2x-3tanx+2=0`

Note that this is quadratic in tan(x).

Thus we can factor as (tanx-2)(tanx-1)=0

By the zero product property we have

(1) tanx=1 ==> `x=pi/4 +kpi` for integer k

(2) tanx=2 ==> `x=tan^(-1)2~~1.107+kpi`

The graph:

pramodpandey | Student





So ,equation reduces to


`y^2-2y -y+2=0`



`` either   y=2 or y=1

if `tan(x)=2`


`x=npi+(7pi)/20`  ,where  n is an integer.

if `tan(x)=1`


`x=n_1pi+pi/4`  ,where `n_1` is an integer.