已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2
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![已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2](/uploads/image/z/5532827-59-7.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%CE%B2%E4%B8%BA%E9%94%90%E8%A7%92%2C%E4%B8%943sin%5E2+%CE%B1%2B2sin%5E2%CE%B2%3D1%2C3sin2%CE%B1-2sin2%CE%B2%3D0%2C%E6%B1%82%E8%AF%81%CE%B1%2B2%CE%B2%3D%CF%80%2F2)
已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2
已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2
已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2
3sin^2α=cos2β 6cosαsinα=2sin2β
所以3sin^2α*2sin2β=6cosαsinαcos2β sinαsin2β=cosαcos2β
所以cos(2β+α)=0 又2β+α∈(0,3π/2) 所以α+2β=π/2