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11. A
用参数方程, P(a/cost, bsint/cost)
14. -1/2
tanθ = -3, 不妨令-π/2 < θ < 0, sinθ < 0, cosθ > 0
tanθ = sin²θ/cos²θ = 9
sin²θ = 9cos²θ = 9(1 - sin²θ)
10sin²θ = 9
sinθ = -3/√10, cosθ = 1/√10
cos²θ + sin2θ = 1/10 + 2sinθcosθ = 1/10 + 2(-3/√10)(1/√10) = 1/10 - 3/5 = -1/2
用参数方程, P(a/cost, bsint/cost)
14. -1/2
tanθ = -3, 不妨令-π/2 < θ < 0, sinθ < 0, cosθ > 0
tanθ = sin²θ/cos²θ = 9
sin²θ = 9cos²θ = 9(1 - sin²θ)
10sin²θ = 9
sinθ = -3/√10, cosθ = 1/√10
cos²θ + sin2θ = 1/10 + 2sinθcosθ = 1/10 + 2(-3/√10)(1/√10) = 1/10 - 3/5 = -1/2
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