若f(sinX)=3-cos2X,则f(cosX)为我是这样做的f(sinx)= 3-(1-2sinx^2)= 2+2sinx^2= 2+2(1-cosx^2)= 4-2conx^2= 4-(con2x+1)= 3-con2x所以f(cosx)= 3- con2x为什么这样做不对呢?
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/03 11:29:29
![若f(sinX)=3-cos2X,则f(cosX)为我是这样做的f(sinx)= 3-(1-2sinx^2)= 2+2sinx^2= 2+2(1-cosx^2)= 4-2conx^2= 4-(con2x+1)= 3-con2x所以f(cosx)= 3- con2x为什么这样做不对呢?](/uploads/image/z/1994788-28-8.jpg?t=%E8%8B%A5f%28sinX%29%3D3-cos2X%2C%E5%88%99f%28cosX%29%E4%B8%BA%E6%88%91%E6%98%AF%E8%BF%99%E6%A0%B7%E5%81%9A%E7%9A%84f%28sinx%29%3D+3-%281-2sinx%5E2%29%3D+2%2B2sinx%5E2%3D+2%2B2%281-cosx%5E2%29%3D+4-2conx%5E2%3D+4-%28con2x%2B1%29%3D+3-con2x%E6%89%80%E4%BB%A5f%28cosx%29%3D+3-+con2x%E4%B8%BA%E4%BB%80%E4%B9%88%E8%BF%99%E6%A0%B7%E5%81%9A%E4%B8%8D%E5%AF%B9%E5%91%A2%3F)
若f(sinX)=3-cos2X,则f(cosX)为我是这样做的f(sinx)= 3-(1-2sinx^2)= 2+2sinx^2= 2+2(1-cosx^2)= 4-2conx^2= 4-(con2x+1)= 3-con2x所以f(cosx)= 3- con2x为什么这样做不对呢?
若f(sinX)=3-cos2X,则f(cosX)为
我是这样做的
f(sinx)= 3-(1-2sinx^2)
= 2+2sinx^2
= 2+2(1-cosx^2)
= 4-2conx^2
= 4-(con2x+1)
= 3-con2x
所以
f(cosx)= 3- con2x
为什么这样做不对呢?
若f(sinX)=3-cos2X,则f(cosX)为我是这样做的f(sinx)= 3-(1-2sinx^2)= 2+2sinx^2= 2+2(1-cosx^2)= 4-2conx^2= 4-(con2x+1)= 3-con2x所以f(cosx)= 3- con2x为什么这样做不对呢?
你的推理过程是:
因为
f(sinx)=3-con2x
所以
f(cosx)=3-con2x
这就相当于说
f(sinx)=f(cosx)
怎么得出来的?
正确的做法如“百墨书生”所说:
令sinx=t
f(sinx)= 3-(1-2sinx^2)
= 2+2sinx^2
则f(t)=2+2t^2
则f(cosx)= 2+2cosx^2
令sinx=t
f(sinx)= 3-(1-2sinx^2)
= 2+2sinx^2
则f(t)=2+2t^2
则f(cosx)= 2+2cosx^2
你脑子抽了
呵呵,你这化来化去还是和题目一样啊,你化到第二步时,就可以得到结果了,只是定义域变了