Question

The solution set of tan theta = 3 cot theta is

Answer 1

Using the reciprocal identity cotθ = 1/tanθ, the equation becomes:
tanθ - 3/tanθ = 0.

Then, multiplying both sides by tanθ (assuming that tanθ ≠ 0 doesn't solve the resulting equation, which it won't) yields:
tan^2 - 3 = 0.

Solving this for tanθ yields tanθ = ±√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.