己知sin^4θ+cos^4θ=5/9,求sin2θ的值

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己知sin^4θ+cos^4θ=5/9,求sin2θ的值己知sin^4θ+cos^4θ=5/9,求sin2θ的值己知sin^4θ+cos^4θ=5/9,求sin2θ的值5/9=(sinx)^4+(co

己知sin^4θ+cos^4θ=5/9,求sin2θ的值
己知sin^4θ+cos^4θ=5/9,求sin2θ的值

己知sin^4θ+cos^4θ=5/9,求sin2θ的值
5/9=(sinx)^4+(cosx)^4=(sin²x+cos²x)²-2(sinxcosx)²=1-2(sinxcosx)².===>2(sinxcosx)²=4/9.===>(sin2x)²=8/9.===>sin2x=±(2√2)/3.