Question

x=asintheta and y=bcostheta... prove:x²/a²+y²/b²=1​

Answer 1

Answer:

Step-by-step explanation:

Squaring both the equations and then adding ,

x²/a² cos²θ + y²/b² sin²θ + 2xy/ab sinθ.cosθ + x²/a² sin²θ + y²/b² cos²θ - 2xy/ab sinθ.cosθ = 2

⇒x²/a² (cos²θ + sin²θ) + y²/b² (sin²θ + cos²θ ) = 2

⇒x²/a² × 1 + y²/b² × 1 = 2 [ ∵ sin²x + cos²x = 1 from trigonometric identities ]

∴ x²/a² + y²/b² = 2 , hence proved

Answer 2

Answer:

x/a = sin theta , y/b = cos Theta , RHS Sin^2 + Cos^2 , which is = 1 as per Pythagoras theorem.