The solution set of tan theta = 3 cot theta is

Joslyn Landry

Joslyn Landry

Answered question


The solution set of tan θ = 3 cot θ is

Answer & Explanation

Eden Pacheco

Eden Pacheco

Beginner2023-03-26Added 4 answers

The equation becomes: using the reciprocal identity cot = 1 tan
tanθ - 3/tanθ = 0
Then, multiplying both sides by tanθ (assuming that tan θ 0 doesn't solve the resulting equation, which it won't) yields:
tan 2 3 = 0.
Solving this for tan θ yields tan θ = ± 3.
From the unit circle, if θ is in [0, 2π], tanθ = -√3 solves to yield θ = 2π/3 and θ = 5π/3 and tanθ = √3 solves to yield θ = π/3 and θ = 4π/3. If you want the general solution, you can get this by adding any multiple of π to these solutions.

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