已知2cos(2x+y)=cosy,求tan(x+y)tany的值
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已知2cos(2x+y)=cosy,求tan(x+y)tany的值
题目有没有问题呢?怎么觉得应该是求tan(x+y)tanx呢?
∵2cos(2x+y)=cosy
∴2cos(x+x+y)=cos(x+y-x)
∴2cosxcos(x+y)-2sinxsin(x+y)=cos(x+y)cosx+sin(x+y)sinx.
移项得
cosxcos(x+y)=3sinxsin(x+y)
两边同时除以cosxcos(x+y),得
3sinxsin(x+y)/cosxcos(x+y)=1.
∴sinxsin(x+y)/cosxcos(x+y)=1/3,
即tan(x+y)tanx=1/3.
∵2cos(2x+y)=cosy
∴2cos(x+x+y)=cos(x+y-x)
∴2cosxcos(x+y)-2sinxsin(x+y)=cos(x+y)cosx+sin(x+y)sinx.
移项得
cosxcos(x+y)=3sinxsin(x+y)
两边同时除以cosxcos(x+y),得
3sinxsin(x+y)/cosxcos(x+y)=1.
∴sinxsin(x+y)/cosxcos(x+y)=1/3,
即tan(x+y)tanx=1/3.
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