If x = a (sin θ + cos θ) and y = b (sin θ

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If x = a (sin θ + cos θ) and y = b (sin θ – cos θ), then the value of
x² +
y² is :
a² b²

x = a (sinθ + cosθ)

⇒	x	= sinθ + cosθ
	a

and, y = b (sinθ – cosθ)

⇒	y	= sinθ - cosθ
	b

∴		x²	+	y²
		a²		b²

= (sinθ + cosθ)² + (sinθ – cosθ)² = 2 (sin²θ + cos²θ) = 2 [∵ (a + b)² + (a – b)² = 2 (a² + b² )]