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# C4 - Parametric equations, Help! watch

1. A curve, C, has parametric equations
x = sinθ - cosθ + 1
y = sin2θ
Show that the cartesian equation of the curve is y = - x^2 + 2x

Could someone show the working for this?
2. y= 2sinθcosθ
y= 1 - (sinθ - cosθ )²
= 1 - (x-1)²
= -x² + 2x
3. (Original post by C4>O7)
y= 2sinθcosθ
y= 1 - (sinθ - cosθ )²
= 1 - (x-1)²
= -x² + 2x
how did you get to the second step?
4. x = sinθ - cosθ + 1
y = sin2θ = 2sinθcosθ

x-1 = sinθ - cosθ
(x-1)² = (sinθ - cosθ )²
x² - 2x + 1 = -2sinθcosθ + sin²θ + cos²θ
x² - 2x + 1 = -2sinθcosθ + 1
x² - 2x = -2sinθcosθ
-x² +2x = 2sinθcosθ

y = -x² + 2x

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