Find the solutions of the equation that are in the interval [0, 2π). (enter your answers as a comma-separated list. if there is no solution, enter no solution.) cot2 θ + cot θ = 0

Question

Mathematics

Ellory

11 August, 17:59

Find the solutions of the equation that are in the interval [0, 2π). (enter your answers as a comma-separated list. if there is no solution, enter no solution.) cot2 θ + cot θ = 0

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Talon Lam · Answer 1

Hello:

cot (2 θ) + cot (θ) = 0

cot (2 θ) = - cot (θ)

cot (2 θ) = cot ( - θ)

2 θ = - θ + 2k π k in : Z

θ = 2k π / 3

in : [0, 2π)

k=0 : θ = 0

k=1 : θ = 2π / 3

k=2 : θ = 4π / 3