`cot^2 (x) - 6cot(x) + 5 = 0` Use inverse functions where needed to find all solutions of the equation in the interval `0,2pi)`.

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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This is a quadratic equation for cot(x). There are two roots,

cot(x) = 1 and cot(x)=5.

Now solve these equations.

On `(0, 2pi)` `cot(x)=1` at `x_1=pi/4` and `x_2=(5pi)/4.`

Also cot(x)=5 at `x_3=cot^(-1)(5)` and `x_4=pi+cot^(-1)(5).`

The answer: `pi/4,`  `(5pi)/4,` `cot^(-1)(5),`  `pi+cot^(-1)(5).`