已知两角差的余弦公式为cos(x+y)=cosxcosy-sinxsiny,由两角差的余弦公式结合诱导公式,推导两角和的正切公式,推导两角和的正切公式tan(x-y)=(tanx-tany)/(1+tanxtany).
问题描述：
已知两角差的余弦公式为cos(x+y)=cosxcosy-sinxsiny,由两角差的余弦公式结合诱导公式,推导两角和的正切公式,推导两角和的正切公式tan(x-y)=(tanx-tany)/(1+tanxtany).
答
cos(x-y)=cosxcosy+sinx+siny
sin(x-y)=cos[90-(x-y)]=sinxcosy-cosxsiny
tan(x-y)=sin(x-y)/cos(x-y)=(tanx-tany)/(1+tanxtany)