已知sinαcosβ=1/2;,试求sinβcosα的取值范围

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已知sinαcosβ=1/2;,试求sinβcosα的取值范围

-1<=sinαcosβ+sinβcosα=sin(α+β)<=1,那么-3/2<=sinβcosα<=1/2 ,而-1<=sinβ<=1,
-1<=cosα<=1,故-1<=sinβcosα<=1,综合上面所述,-1<=sinβcosα<=1/2