sinα^2+sinβ^2+sinγ^2=1,那么cosαcosβcosγ最大值等于
问题描述：
sinα^2+sinβ^2+sinγ^2=1,那么cosαcosβcosγ最大值等于
答
令 x =cos α,y =cos β,z =cos γ,则 1 =(sin α)^2 +(sin β)^2 +(sin γ)^2=(1 -x^2) +(1 -y^2) +(1 -z^2)=3 -(x^2 +y^2 +z^2),所以 x^2 +y^2 +z^2 =2.由基本不等式,三次根号 (x^2 *y^2 *z^2) ≤ (x^2 +y^2 +z^2)...