已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4）的值

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已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4）的值已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求si

已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4）的值
已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4）的值

已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4）的值
7√2/10
详情见

sin(x-y)cosx-cos(y-x)sinx=3/5,
即sin(x-y)cosx-cos(x-y)sinx=3/5,
sin[(x-y)-x] =3/5,
sin(-y)= 3/5,
siny= -3/5.
y是第三象限角,所以cosy=-4/5.
sin(y+5π/4）=-sin(y+π/4)
=-(sin y cosπ/4+cos y sinπ/4)
=7√2/10.

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