2017 · Q61
If x sinθ = y cosθ = (2z tanθ)/(1-tan²θ), then what is 4z²(x²+y²) equal to ?
Elementary MathematicsTrigonometry
- A(x² + y²)³
- B(x² - y²)²
- C(x² - y²)³
- D(x² + y²)²
Explanation
From x sinθ = y cosθ, tanθ = y/x. Also 2z tanθ/(1−tan²θ) = z·tan2θ = 2xyz/(x²−y²), so x sinθ = 2xyz/(x²−y²): sinθ = 2yz/(x²−y²), cosθ = 2xz/(x²−y²). Then sin²θ + cos²θ = 1 gives 4z²(x²+y²) = (x²−y²)²: option B.