2025 · Q30
If m²(sin θ−1) + n^(2 )(sin θ + 1)=0 , where (π )/(2), then what is (m^(2 )+ n²) cosθ−(m^(2 )− n²) cot θ equal to?
Elementary MathematicsTrigonometry
- A4 mn
- B2 mn
- C1
- D0
Explanation
From m²(sinθ−1) + n²(sinθ+1) = 0 we get (m²+n²)sinθ = m²−n², so sinθ = (m²−n²)/(m²+n²). Then (m²+n²)cosθ − (m²−n²)cotθ = cosθ[(m²+n²) − (m²−n²)/sinθ] = cosθ[(m²+n²) − (m²+n²)] = 0, option (d).