2016 · Q97
If tanθ + cotθ = 4/√3, where 0 < θ < π/2, then sinθ + cosθ is equal to
Elementary MathematicsTrigonometry
- A1
- B(√(3) - 1)/2
- C(√(3) + 1)/2
- D√(3)
Explanation
Put s = sinθ+cosθ: then s² = 1+2sinθcosθ = 1+2/(tanθ+cotθ) = 1+2/(4/√3) = 1+√3/2. Since 0 < θ < π/2, s > 0. Thus s = √((2+√3)/2) = (√3+1)/2, option C.