已知sinθ-cosθ=1/3,则sin^2θ的值为

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已知sinθ-cosθ=1/3,则sin^2θ的值为

已知sinθ-cosθ=1/3,则sin^2θ的值为
已知sinθ-cosθ=1/3,则sin^2θ的值为

已知sinθ-cosθ=1/3,则sin^2θ的值为
sinθ-cosθ=1/3
sinθ-1/3=cosθ
(sinθ-1/3)^2=(cosθ)^2
(sinθ)^2-2/3 sinθ +1/9 =1- (sinθ)^2
2(sinθ)^2-2/3 sinθ -8/9 = 0
(sinθ)^2-1/3 sinθ -4/9 = 0
(sinθ+1/3)(sinθ-4/3) = 0
∵-1≤sinθ≤1
∴sinθ-4/3<0
∴sinθ+1/3=0
∴sinθ=-1/3
∴sin^2θ=1/9

sin2θ=72/81