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.

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|