高一三角函数一道化简问题
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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
![高一三角函数一道化简问题](/uploads/image/z/19367971-43-1.jpg?t=%E9%AB%98%E4%B8%80%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E4%B8%80%E9%81%93%E5%8C%96%E7%AE%80%E9%97%AE%E9%A2%98)
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)