if x/a cos A + x/b sin A =1 & x/a sin A - y/b cos A =1 then P.T x/a^2 + y/b^2
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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
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
jvs5:
but
but
in qestion there is no X^2
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