`tan^2 (x) - tan(x) - 2 = 0` Use inverse functions where needed to find all solutions of the equation in the interval `0,2pi)`.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

This is the quadratic equation for tan(x). It has roots -1 and 2.

tan(x)=-1 on `(0, 2pi)` at `x_1=(3pi)/4` and `x_2=(7pi)/4.`

tan(x)=2 on `(0, 2pi)` at `x_3=tan^(-1)(2)` and `x_4=pi+tan^(-1)(2).`

There are 4 roots at all.