Question

If x = a cos θ + sin θ. y = a sin θ – b cos θ. Show that x² + y² = a² + b² 

Answer 1

Consider x² = (acosθ + bsin θ)² 

⇒ x² = a²cos²θ + 2abcosθsinθ + b²sin²θ …….(1) 

Again consider y² = (asinθ – bcosθ)² 

⇒ y² = a²sin²θ – abcosθ sinθ + b²cos²θ …….. (2) 

(1) + (2) ⇒ x² + y² = a² + b²