2020 · Q46
If cosec θ − sin θ = m and sec θ − cos θ = n, then what is m⁴ᐟ³n²ᐟ³ + m²ᐟ³n⁴ᐟ³ equal to?
Elementary MathematicsTrigonometry
- A0
- B1
- Cmn
- Dm²n²
Explanation
m = cos^2(theta)/sin(theta) and n = sin^2(theta)/cos(theta). The expression equals (mn)^(2/3)*(m^(2/3)+n^(2/3)) = (sin(theta)cos(theta))^(2/3) * 1/(sin(theta)cos(theta))^(2/3) = 1. Hence option (B).