函数y=cosx/(1-sinx)的单调递增区间思路我知道:cosx=cos(x/2)平方-sin(x/2)平方1-sinx=cos(x/2)平方 -2sin(x/2)cos(x/2)+sin(x/2)平方=[cos(x/2)-sin(x/2)]平方所以y=cos(x/2)平方-sin(x/2)平方 / [cos(x/2)-sin(x/2)]平方=cos(x/2)+
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 17:59:02
![函数y=cosx/(1-sinx)的单调递增区间思路我知道:cosx=cos(x/2)平方-sin(x/2)平方1-sinx=cos(x/2)平方 -2sin(x/2)cos(x/2)+sin(x/2)平方=[cos(x/2)-sin(x/2)]平方所以y=cos(x/2)平方-sin(x/2)平方 / [cos(x/2)-sin(x/2)]平方=cos(x/2)+](/uploads/image/z/1699833-57-3.jpg?t=%E5%87%BD%E6%95%B0y%3Dcosx%2F%281-sinx%29%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4%E6%80%9D%E8%B7%AF%E6%88%91%E7%9F%A5%E9%81%93%EF%BC%9Acosx%3Dcos%28x%2F2%29%E5%B9%B3%E6%96%B9-sin%28x%2F2%29%E5%B9%B3%E6%96%B91-sinx%3Dcos%28x%2F2%29%E5%B9%B3%E6%96%B9+-2sin%28x%2F2%29cos%28x%2F2%29%2Bsin%28x%2F2%29%E5%B9%B3%E6%96%B9%3D%5Bcos%28x%2F2%29-sin%28x%2F2%29%5D%E5%B9%B3%E6%96%B9%E6%89%80%E4%BB%A5y%3Dcos%28x%2F2%29%E5%B9%B3%E6%96%B9-sin%28x%2F2%29%E5%B9%B3%E6%96%B9+%2F+%5Bcos%28x%2F2%29-sin%28x%2F2%29%5D%E5%B9%B3%E6%96%B9%3Dcos%28x%2F2%29%2B)
函数y=cosx/(1-sinx)的单调递增区间思路我知道:cosx=cos(x/2)平方-sin(x/2)平方1-sinx=cos(x/2)平方 -2sin(x/2)cos(x/2)+sin(x/2)平方=[cos(x/2)-sin(x/2)]平方所以y=cos(x/2)平方-sin(x/2)平方 / [cos(x/2)-sin(x/2)]平方=cos(x/2)+
函数y=cosx/(1-sinx)的单调递增区间
思路我知道:
cosx=cos(x/2)平方-sin(x/2)平方
1-sinx=cos(x/2)平方 -2sin(x/2)cos(x/2)+sin(x/2)平方
=[cos(x/2)-sin(x/2)]平方
所以y=cos(x/2)平方-sin(x/2)平方 / [cos(x/2)-sin(x/2)]平方
=cos(x/2)+sin(x/2) / cos(x/2)-sin(x/2)
=1+tan(x/2) / 1-tan(x/2)
我主要是卡在这一步:
所以y=cos(x/2)平方-sin(x/2)平方 / [cos(x/2)-sin(x/2)]平方
=cos(x/2)+sin(x/2) / cos(x/2)-sin(x/2)
=1+tan(x/2) / 1-tan(x/2)
为什么可以直接就把平方去掉?我代数值进去不能成立的啊!
函数y=cosx/(1-sinx)的单调递增区间思路我知道:cosx=cos(x/2)平方-sin(x/2)平方1-sinx=cos(x/2)平方 -2sin(x/2)cos(x/2)+sin(x/2)平方=[cos(x/2)-sin(x/2)]平方所以y=cos(x/2)平方-sin(x/2)平方 / [cos(x/2)-sin(x/2)]平方=cos(x/2)+
这里不是把平方去掉,是
y=cos(x/2)平方-sin(x/2)平方 / [cos(x/2)-sin(x/2)]平方
=(cos(x/2)-sin(x/2))(cos(x/2)+sin(x/2))/[cos(x/2)-sin(x/2)]平方
=cos(x/2)+sin(x/2) / cos(x/2)-sin(x/2) 约分
y=cos(x/2)平方-sin(x/2)平方 / [cos(x/2)-sin(x/2)]平方
=(cosx/2+sinx/2)(cosx/2-sinx/2)/(cosx/2-sinx/2)²
=(cosx/2+sinx/2)/(cosx/2-sinx/2)
分子利用平方差公式。
分子可分解为平方差公式,消掉就能成立