已知sin(x-y)cosx-cos(x-y)sinx=五分之三求tan2y的值

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已知sin(x-y)cosx-cos(x-y)sinx=五分之三求tan2y的值

已知sin(x-y)cosx-cos(x-y)sinx=五分之三求tan2y的值
已知sin(x-y)cosx-cos(x-y)sinx=五分之三求tan2y的值

已知sin(x-y)cosx-cos(x-y)sinx=五分之三求tan2y的值
sin(x-y)cosx-cos(x-y)sinx
=sin[(x-y)-x]
=sin(-y)
=-siny=3/5
siny=-3/5
sin²y+cos²y=1
所以cos²y=16/25
cosy=4/5或-4/5
tany=siny/cosy=-3/4或3/4
tan2y=2tany/(1-tan²y)=±(3/2)/(1-9/16)=±8/3

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