:请高手帮忙啊 若α∈(0,π/2),a?b?o,求f(α)=a^2/(cosα)^2 b^2/(sinα)^2的最小值要过程啊
请高手帮忙啊 若α∈(0,π/2),a?b?o,求f(α)=a^2/(cosα)^2+b^2/(sinα)^2的最小值要过程啊
若α∈(0,π/2),a?b?o,求f(α)=a^2/(cosα)^2+b^2/(sinα)^2的最小值 f(α)=a^2/(cosα)^2+b^2/(sinα)^2=a^2*[1+(tanα)^2]+b^2*[1+(cotα)^2] =a^2 +b^2 + (a*tanα)^2 + (b*cotα)^2 ≥a^2+b^2 + 2ab (均值不等式) 所以(tanα)^2=b/a 时,f(α)的最小值为:(a+b)^2
答:受yexiao1990maths老师留言的启发,得以下证明方法: ∵sinθ=2ab/(a^2+b^2),且0b, ∴cosθ=根[1-(sinθ)^2]=(a...详情>>
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