2021 · Q43
If cosec θ − cot θ = m, then what is cosec θ equal to?
Elementary MathematicsTrigonometry
- A(m + 1)/m
- B(m − 1)/m
- C(m² + 2)/2m
- D(m² + 1)/2m
Explanation
Since (cosecθ − cotθ)(cosecθ + cotθ) = cosec²θ − cot²θ = 1, we have cosecθ + cotθ = 1/m. Adding this to cosecθ − cotθ = m gives 2cosecθ = m + 1/m = (m²+1)/m. Thus cosecθ = (m²+1)/(2m). Hence option D.