设α、β属于[-π/2,π/2],满足不等式sinαcosβ+sinβcosα=1,则sinα+sinβ的取值范围
问题描述:
设α、β属于[-π/2,π/2],满足不等式sinαcosβ+sinβcosα=1,则sinα+sinβ的取值范围
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答
∵α、β属于[-π/2,π/2],则α+β∈[-π,π],sinαcosβ+sinβcosα=sin(α+β)=1∴α+β=π/2∴sinα+sinβ=sinα+sin(π/2-α)=sinα+cosα=√2sin(π/4+α)∵α属于[-π/2,π/2]∴π/4+α∈[-π/4,3π/4]∴sin(...