2023 · Q27
Which one of the following is a value of θ, if θ satisfies the equation tan 2θ tan 4θ − 1 = 0; 0 < θ < π/2?
Elementary MathematicsTrigonometry
- Aπ/12
- Bπ/15
- Cπ/6
- Dπ/5
Explanation
From tan2θ·tan4θ = 1 we get tan4θ = cot2θ = tan(π/2 − 2θ). In the range 0 < θ < π/2 the principal solution gives 4θ = π/2 − 2θ, so 6θ = π/2 and θ = π/12. Checking: tan(π/6)·tan(π/3) = (1/√3)(√3) = 1. Among the options only (A) π/12 satisfies the equation.