The elimination of θ from x cos θ - y sin θ = 2 and x sin θ + y cos θ = 4 will give:
Answer & explanation
Correct answer: option 2
x cos θ - y sin θ = 2
On squaring both sides
x² cos²θ + y² sin²θ - 2xy sinθ cosθ = 4 ---------(1)
And, x sin θ + y cos θ = 4
x² sin²θ + y² cos²θ + 2xy sinθ cosθ = 16 ------(2)
On adding 1 and 2 ,
x² ( cos²θ+ sin²θ ) + y² ( sin²θ + cos²θ) = 4 + 16 = 20
x² + y² = 20