# `cot^2 (x) - 9 = 0` Use inverse functions where needed to find all solutions of the equation in the interval `0,2pi)`.

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Borys Shumyatskiy | Certified Educator

`cot^2(x)=9,`

cot(x)=3 or cot(x)=-3.

The general solution for cot(x)=a is

On `(0, 2pi)` there are `cot^(-1)(3), cot^(-1)(3)+pi, pi-cot^(-1)(3), 2pi-cot^(-1)(3).`

Note that `cot^(-1)(-3)=-cot^(-1)(3).`