2014 · Q62
If sin θ + 2 cos θ = 1, where 0 < θ < π/2, then what is 2 sin θ - cos θ equal to?
Elementary MathematicsTrigonometry
- A-1
- B1/2
- C2
- D1
Explanation
Squaring (sinθ+2cosθ)^2 + (2sinθ-cosθ)^2 = 5 gives (2sinθ-cosθ)^2 = 4; positive root 2.
If sin θ + 2 cos θ = 1, where 0 < θ < π/2, then what is 2 sin θ - cos θ equal to?
Explanation
Squaring (sinθ+2cosθ)^2 + (2sinθ-cosθ)^2 = 5 gives (2sinθ-cosθ)^2 = 4; positive root 2.