已知x+y=√3sin(θ-π/4),x-y=√3sin(θ+π/4),求x²+y²的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/21 22:16:33
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+y

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

已知x+y=√3sin(θ-π/4),x-y=√3sin(θ+π/4),求x²+y²的值
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