2014 · Q54
If 0 < θ < π/4, then what is √(1 − 2 sin θ cos θ) equal to?
Elementary MathematicsTrigonometry
- Acos θ − sin θ
- Bsin θ − cos θ
- C±(cos θ − sin θ)
- Dcos θ sin θ
Explanation
1 − 2 sin θ cos θ = (cos θ − sin θ)²; the root is |cos θ − sin θ| = cos θ − sin θ since cos θ > sin θ on (0, π/4).