2019 · Q57
If 3tanθ = cotθ where 0 ≤ θ ≤ π/2, then what is the value of θ?
Elementary MathematicsTrigonometry
- Aπ/6
- Bπ/4
- Cπ/3
- Dπ/2
Explanation
From 3 tan(theta) = cot(theta) = 1/tan(theta) we get 3 tan^2(theta) = 1, i.e. tan^2(theta) = 1/3. On [0, pi/2] the tangent is non-negative, so tan(theta) = 1/sqrt(3). The angle in [0, pi/2] with tangent 1/sqrt(3) is pi/6. Hence theta = pi/6, option (a).