Question

高一数学必修4第4题 x+y=√2sin(θ+π/4),x-y=√2sin(θ-π/4),求证x^+y^1 请问如何解?

Answer 1

x+y=√2 sin(θ+π/4),x-y=√2 sin(θ-π/4),

（X+Y)^2=2 sin^2(θ+π/4)

(X-Y)^2=2sin^2(θ-π/4)=2COS^2[π/4+(θ-π/4)]=2 cos^2(θ+π/4)

（X+Y)^2+(X-Y)^2=2(x^2+y^2)=2 sin^2(θ+π/4)+2 cos^2(θ+π/4)

(x^2+y^2)= sin^2(θ+π/4)+cos^2(θ+π/4)=1