作业帮高一三角函数一道化简问题
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/07/18 11:04:12
高一三角函数一道化简问题
[siny+sinxcos(x+y)]/[cosy-sinxsin〔x+y〕]
化简
[siny+sinxcos(x+y)]/[cosy-sinxsin〔x+y〕]
化简
siny+sinxcos(x+y)
=siny+sinx(cosxcosy-sinxsiny)
=siny+sinxcosxcosy-siny*(sinx)^2
=siny[1-(sinx)^2]+sinxcosxcosy
=sinycosx^2+sinxcosxcosy
=cosx(sinycosx+sinxcosy)
=cosxsin(x+y)
同理,计算可以得到
cosy-sinxsin(x+y)
=cosxcos(x+y)
所以
原式=tan(x+y)
=siny+sinx(cosxcosy-sinxsiny)
=siny+sinxcosxcosy-siny*(sinx)^2
=siny[1-(sinx)^2]+sinxcosxcosy
=sinycosx^2+sinxcosxcosy
=cosx(sinycosx+sinxcosy)
=cosxsin(x+y)
同理,计算可以得到
cosy-sinxsin(x+y)
=cosxcos(x+y)
所以
原式=tan(x+y)