已知x+y=√3sin(θ-π/4),x-y=√3sin(θ+π/4),求x²+y²的值
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已知x+y=√3sin(θ-π/4),x-y=√3sin(θ+π/4),求x²+y²的值
![已知x+y=√3sin(θ-π/4),x-y=√3sin(θ+π/4),求x²+y²的值](/uploads/image/z/17243275-67-5.jpg?t=%E5%B7%B2%E7%9F%A5x%2By%3D%E2%88%9A3sin%28%CE%B8-%CF%80%2F4%29%2Cx-y%3D%E2%88%9A3sin%28%CE%B8%2B%CF%80%2F4%29%2C%E6%B1%82x%26%23178%3B%2By%26%23178%3B%E7%9A%84%E5%80%BC)
x+y=√3sin(θ-π/4) = √3(sinθ*√2/2 - cosθ*√2/2) = (√6/2)(sinθ - cosθ)
x-y=√3sin(θ+π/4) = √3(sinθ*√2/2 + cosθ*√2/2) = (√6/2)(sinθ + cosθ)
相加2x = √6sinθ, x= (√6/2)sinθ
相减2y = -√6cosθ, y= -(√6/2)cosθ
x²+y² = (6/4)(sin²θ + cos²θ) = 3/2
x-y=√3sin(θ+π/4) = √3(sinθ*√2/2 + cosθ*√2/2) = (√6/2)(sinθ + cosθ)
相加2x = √6sinθ, x= (√6/2)sinθ
相减2y = -√6cosθ, y= -(√6/2)cosθ
x²+y² = (6/4)(sin²θ + cos²θ) = 3/2
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