2018 · Q61
If cosθ = 1/√5, where 0 < θ < π/2, then 2tanθ/(1 - tan²θ) is equal to
Elementary MathematicsTrigonometry
- A4/3
- B-4/3
- C1/3
- D-2/3
Explanation
cos(theta) = 1/sqrt(5) with theta acute gives sin(theta) = 2/sqrt(5), so tan(theta) = 2. Then 2 tan(theta)/(1 - tan^2(theta)) = 4/(1 - 4) = -4/3. Hence option B.