设α,β,γ∈(0,π/2)且(sinα)^2+(sinβ)^2+(sinγ)^2=1求函数y=(sinα)^3/sinβ+(sinβ)^3/sinγ+(sinγ)^3/sinα 的最小值.

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设α,β,γ∈(0,π/2)且(sinα)^2+(sinβ)^2+(sinγ)^2=1求函数y=(sinα)^3/sinβ+(sinβ)^3/sinγ+(sinγ)^3/sinα的最小值.设α,β,γ

设α,β,γ∈(0,π/2)且(sinα)^2+(sinβ)^2+(sinγ)^2=1求函数y=(sinα)^3/sinβ+(sinβ)^3/sinγ+(sinγ)^3/sinα 的最小值.
设α,β,γ∈(0,π/2)
且(sinα)^2+(sinβ)^2+(sinγ)^2=1
求函数y=(sinα)^3/sinβ+(sinβ)^3/sinγ+(sinγ)^3/sinα 的最小值.

设α,β,γ∈(0,π/2)且(sinα)^2+(sinβ)^2+(sinγ)^2=1求函数y=(sinα)^3/sinβ+(sinβ)^3/sinγ+(sinγ)^3/sinα 的最小值.
(sinα)^3/sinβ+(sinα)^3/sinβ+(sinβ)^2≥3(sinα)^2
(sinβ)^3/sinγ+(sinβ)^3/sinγ+(sinγ)^2≥3(sinβ)^2
(sinγ)^3/sinα+(sinγ)^3/sinα+(sinα)^2≥3(sinγ)^2
y=(sinα)^3/sinβ+(sinβ)^3/sinγ+(sinγ)^3/sinα≥1

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