2018 · Q70
If cotθ(1 + sinθ) = 4m and cotθ(1 - sinθ) = 4n, then which one of the following is correct?
Elementary MathematicsTrigonometry
- A(m² + n²)² = mn
- B(m² - n²)² = mn
- C(m² - n²)² = m²n²
- D(m² + n²)² = m²n²
Explanation
mn = cot^2(theta)(1 - sin^2(theta))/16 = cot^2(theta) cos^2(theta)/16 = cos^4(theta)/(16 sin^2(theta)). Also m^2 - n^2 = (m - n)(m + n) = (2 sin(theta) cot(theta))(2 cot(theta))/16 = cos^2(theta)/(4 sin(theta)). Squaring gives (m^2 - n^2)^2 = cos^4(theta)/(16 sin^2(theta)) = mn. Hence option B.