Question

X= Sinθ+Cosθ , Y= Sinθ-Cosθ eliminate θ

Answer 1

Answer:

X² + Y² = 2

Step-by-step explanation:

= > X = sinθ + cosθ

Square on both sides:

= > X² = ( sinθ + cosθ )²

= > X² = sin²θ + cos²θ + 2sinθcosθ

Similarly,

= > Y² = ( sinθ - cosθ )²

= > Y² = sin²θ + cos²θ - 2sinθcosθ

Adding X² and Y²

= > X² + Y² = sin²θ + cos²θ + 2sinθcosθ + sin²θ + cos²θ - 2sinθcosθ

= > X² + Y² = sin²θ + cos²θ + sin²θ + cos²θ

= > X² + Y² = 2( sin²θ + cos²θ )

= > X² + Y² = 2(1) = 2

= > X² + Y² = 2