已知α,β,γ为锐角,sin²α+sin²β+sin²γ=1.求证π/2<α+β+γ<3π/4
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![已知α,β,γ为锐角,sin²α+sin²β+sin²γ=1.求证π/2<α+β+γ<3π/4](/uploads/image/z/15155430-6-0.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%2C%CE%B2%2C%CE%B3%E4%B8%BA%E9%94%90%E8%A7%92%2Csin%26%23178%3B%CE%B1%EF%BC%8Bsin%26%23178%3B%CE%B2%EF%BC%8Bsin%26%23178%3B%CE%B3%EF%BC%9D1.%E6%B1%82%E8%AF%81%CF%80%2F2%EF%BC%9C%CE%B1%EF%BC%8B%CE%B2%EF%BC%8B%CE%B3%EF%BC%9C3%CF%80%2F4)
已知α,β,γ为锐角,sin²α+sin²β+sin²γ=1.求证π/2<α+β+γ<3π/4
已知α,β,γ为锐角,sin²α+sin²β+sin²γ=1.求证π/2<α+β+γ<3π/4
已知α,β,γ为锐角,sin²α+sin²β+sin²γ=1.求证π/2<α+β+γ<3π/4
sin²α+sin²β+sin²γ=1,
∴2sin²γ=2-2sin^α-2sin²β
=cos2α+cos2β
=2cos(α+β)cos(α-β),①
α,β,γ是锐角,
∴0cos(α+β)>0,
∴|α-β|