设α,β,γ∈(0,π/2)
问题描述：
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.
答
(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