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=3/5siny=-3/5sin²y+cos²y=1所以cos²y=16/25cosy=4/5或-4/5tany=siny/cosy=-3/4或3/4tan2y=2tany/(1-tan²y)=±(3/2)/(1-9/16)=±8/3