已知sin(x+π/6)=1/4,求sin(5π/6-x)+sin^2(π/3-x)

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已知sin(x+π/6)=1/4,求sin(5π/6-x)+sin^2(π/3-x)

已知sin(x+π/6)=1/4,求sin(5π/6-x)+sin^2(π/3-x)
已知sin(x+π/6)=1/4,求sin(5π/6-x)+sin^2(π/3-x)

已知sin(x+π/6)=1/4,求sin(5π/6-x)+sin^2(π/3-x)
sin(5π/6-x)=sin(π-(x+π/6))=sin(x+π/6)=1/4
sin(π/3-x)=sin(5π/6-x-π/2)=-cos(5π/6-x)
sin^2(π/3-x)=cos^2(5π/6-x)=1-(1/4)^2=15/16
sin(5π/6-x)+sin^2(π/3-x)=1/4+15/16=19/16

sin(5π/6-x)=sin[π-(π/6+x)]=sin(x+π/6)=1/4,
由cos2A=1-2sin^A
sin^2(π/3-x)=1/2-1/2*cos(π/3+2x)=1/2-1/2[1-2(1/4)^2]=1/16
所以结果为5/16

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