已知sin(45°-α)=-1/2,45°

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已知sin(45°-α)=-1/2,45°已知sin(45°-α)=-1/2,45°已知sin(45°-α)=-1/2,45°sin(45°-α)=-1/2sin(α-45º)=1/245°

已知sin(45°-α)=-1/2,45°
已知sin(45°-α)=-1/2,45°<α<90°,则sinα=

已知sin(45°-α)=-1/2,45°
sin(45°-α)=-1/2
sin(α-45º)=1/2 45°<α<90°
α-45º=30º
α=75º
sinα=sinα75º=sin(30º+45º)=1/2x√2/2+∨3/2x√2/2=(√2+√6)/4

45<α<90
则-45<45-α<0
sin (45-α)=-1/2
所以45-α=-30
α=75
所以原式=sin(45+30)
=sin45cos30+cos45sin30
=(√6+√2)/2