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

Textbook Question

Chapter 5, 5.3 - Problem 64 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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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.

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