2017 · Q48
If sin θ = (m² − n²)/(m² + n²) and 0 < θ < π/2, then what is the value of cos θ ?
Elementary MathematicsTrigonometry
- A2mn/(m² + n²)
- B2mn/(m² - n²)
- C(m² + n²)/2mn
- D(m² - n²)/2mn
Explanation
cos²θ = 1−sin²θ = [(m²+n²)²−(m²−n²)²]/(m²+n²)² = 4m²n²/(m²+n²)². With 0 < θ < π/2, cos θ > 0, so cos θ = 2mn/(m²+n²). Hence option (A). (Trap: option (B) drops the square in the denominator.)