已知tanx=4/3,x在(π,3/2π),若tany=1/2,求证 cos(x-y)=2sin(x-y)
问题描述：
已知tanx=4/3,x在(π,3/2π),若tany=1/2,求证 cos(x-y)=2sin(x-y)
答
tanx=4/3，tany=1/2，则tan(x－y)=[tanx－tany]/[1＋tanxtany]=[(4/3)－(1/2)]/[1＋(4/3)(1/2)]=1/2，即[sin(x－y)]/[cos(x－y)]=1/2，则cos(x－y)=2sin(x－y)
答
tan(x-y)=[tanx-tany]/[1+tanx*tany]
=(4/3-1/2)/(1+4/3*1/2)=1/2
即sin(x-y) /cos(x-y)=1/2,
故cos(x-y)=2sin(x-y)
答
一楼最佳答案
tan(x-y)=(tanx-tany)/(1+tanxtany)=1/2
cos(x-y)=2sin(x-y)