2025 · Q26
What is (sinθ )/(1-cotθ )+(cosθ )/(1-tanθ ) (θ ≠ π/4) equal to?
Elementary MathematicsTrigonometry
- Asin θ + cos θ
- Bsin θ − cos θ
- Ccos θ − sin θ
- D− (sin θ + cos θ)
Explanation
Write 1 − cotθ = (sinθ − cosθ)/sinθ and 1 − tanθ = (cosθ − sinθ)/cosθ. The first term becomes sin²θ/(sinθ − cosθ) and the second −cos²θ/(sinθ − cosθ). Their sum is (sin²θ − cos²θ)/(sinθ − cosθ) = sinθ + cosθ, option (a).