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If x = a sin θ – b cos θ, y = a cos θ + b sin θ, then which of the following is true?
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x² + a² = 1 y² b² - x² + y² = a² – b²
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x² + y² = 1 a² b² - x² + y² = a² + b²
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Correct Option: D
x = a sinθ – b cosθ --- (i)
y = a cosθ + b sinθ - (ii)
On squaring and adding both the equations,
x² + y² = (a sinθ – b cosθ)² + (a cosθ + b sinθ)²
= a² sin²θ + b² cos²θ – 2ab sinθ . cosθ + a² cos²θ + b² sin²θ + 2ab sinθ . cosθ
= a² (sin²θ + cos²θ) + b² (cos²θ + sin²θ)
= a² + b² [∵ sin²θ + cos²θ = 1]
