y=sin(a)*cos(a)^2不用导数求其最值

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y=sin(a)*cos(a)^2不用导数求其最值
y=sin(a)*cos(a)^2不用导数求其最值

y=sin(a)*cos(a)^2不用导数求其最值
y=sinα(cosα)^2
即y^2=(1/2)·2(sinα)^2·(cosα)^2·(cosα)^2
≤(1/2)·[(2(sinα)^2+(cosα)^2+(cosα)^2)/3]^3
=(1/2)·(2/3)^3
=4/27
∴2(sinα)^2=(cosα)^2,即tanα=√2/2时,
所求最大值为:y|max=(2√3)/9.