Đáp án:

Giải thích các bước giải:

ĐK: `cosx ne 0 <=> x ne pi/2 + kpi, k in ZZ`

 `tan^3x + 2tanx + 3 = 3/(cos^2x)`

`<=> tan^3x + 2tanx + 3 = 3(1 + tan^2x)`

`<=> tan^3x + 2tanx + 3 = 3 + 3tan^2x`

`<=> tan^3x - 3tan^2x + 2tanx = 0`

`<=> tanx(tan^2x - 3tanx + 2) = 0`

`<=> tanx(tanx - 1)(tanx - 2) = 0`

`<=>` `[ (tanx = 0), (tanx = 1), (tanx = 2) :}`

`<=>` `[ (x = kpi), (x = pi/4 + kpi), (x = arctan(2) + kpi) :}` `(k in ZZ)`