2024 · Q17
If cosecθ - cotθ = m and secθ - tanθ = n, then what is cosecθ + secθ equal to?
Elementary MathematicsTrigonometry
- A1/2 (m + n + 1/m+1/n)
- B(m + n + 1/m+1/n)
- C1/2 (m + n - 1/m-1/n)
- D(m + n - 1/m-1/n)
Explanation
Since (cosecθ−cotθ)(cosecθ+cotθ) = cosec²θ−cot²θ = 1, we get cosecθ+cotθ = 1/m. Similarly (secθ−tanθ)(secθ+tanθ) = 1 gives secθ+tanθ = 1/n. Solving: cosecθ = (m+1/m)/2 and secθ = (n+1/n)/2. Adding gives ½(m + n + 1/m + 1/n) — option A.