Question

已知X+Y=根号3sin(θ-π/4)，X-Y=根号3sin(θ+π/4)，求X�0�5+Y�0�5

Answer 1

X+Y=√3sin(θ-π/4)
X-Y=√3sin(θ+π/4)
2x=√3[sin(θ-π/4)+sin(θ+π/4)]
sin(θ-π/4)+sin(θ+π/4)=2sinθcosπ/4=√2sinθ
x=√6sinθ/2
2y=√3[sin(θ-π/4)-sin(θ+π/4)]
sin(θ-π/4)-sin(θ+π/4)=-2cosθsinπ/4
y=-√6cosθ/2

X�0�5+Y�0�5
不知道啥意思

Answer 2

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
x�0�5+y�0�5 = (6/4)(sin�0�5θ + cos�0�5θ) = 3/2