2016 · Q62
If x/a - y/b tanθ = 1 and x/a tanθ + y/b = 1, then the value of x²/a² + y²/b² is
Elementary MathematicsTrigonometry
- A2sec²θ
- Bsec²θ
- Ccos²θ
- D2cos²θ
Explanation
Put X = x/a, Y = y/b, t = tanθ: the equations become X−Yt = 1 and Xt+Y = 1. Squaring and adding gives (1+t²)(X²+Y²) = 2. Hence x²/a²+y²/b² = 2/(1+tan²θ) = 2cos²θ, option D.