Question

PLEASE HELP me with this question...

Answer 1

Given : xcosθ - ysinθ = a

Squaring on both sides, We get :

⇒ (xcosθ - ysinθ)² = a²

⇒ x²cos²θ + y²sin²θ - 2xycosθsinθ = a² ------------------ [1]

Given : xsinθ + ycosθ = b

Squaring on both sides, We get :

⇒ (xsinθ + ycosθ)² = b²

⇒ x²sin²θ + y²cos²θ + 2xycosθsinθ = b² ------------------ [2]

Adding both Equation's [1] and [2], We get :

⇒ (x²cos²θ + y²sin²θ) - 2xycosθsinθ + (x²sin²θ + y²cos²θ) + 2xycosθsinθ  = (a² + b²)

⇒ (x²cos²θ + y²sin²θ) + (x²sin²θ + y²cos²θ) = a² + b²

⇒ x²(sin²θ + cos²θ) + y²(sin²θ + cos²θ) = a² + b²

We know that : (sin²θ + cos²θ) = 1

⇒ x² + y² = a² + b²