Question

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

Answer 1

(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