2016 · Q68
Which of the following is correct in respect of the equation 3-tan²θ =α(1-3tan²θ)? (Given that α is a real number.)
Elementary MathematicsTrigonometry
- Aα∈[1/3,3]
- Bα∈(-∞,1/3]∪[3,∞]
- Cα∈(-∞,1/3)∪[3,∞)
- DNone of the above
Explanation
With t = tan²θ ≥ 0 (t ≠ 1/3), α = (3−t)/(1−3t), which is increasing on each interval. On [0,1/3) it ranges over [3,∞), and on (1/3,∞) over (−∞,1/3). Hence α ∈ (−∞,1/3)∪[3,∞), option C.