3tanx=2tan(2x+y) 求证：sin（2x+y）=5siny

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/10/04 19:49:02

3tanx=2tan(2x+y)
两边同乘以cosx cos(2x+y)：
3sinx cos(2x+y) = 2sin(2x+y) cosx
6sinx cos(2x+y) = 4sin(2x+y) cosx
6sinx cos(2x+y) + sinx cos(2x+y) = 4sin(2x+y) cosx - sin(2x+y) cosx
sinx cos(2x+y) + sin(2x+y) cosx = 5sin(2x+y) cosx - 5sinx cos(2x+y)
sinx cos(2x+y) + cosx sin(2x+y) = 5sin(2x+y) cosx - 5cos(2x+y)sinx
sin(x+2x+y) = 5 sin(2x+y-x)
sin[2(x+y)] = 5 sin(x+y)
题目条件不正确.
如果条件改为【3tanx=2tan(x+y) 】
两边同乘以cosx cos(x+y)：
3sinx cos(x+y) = 2sin(x+y) cosx
6sinx cos(x+y) = 4sin(x+y) cosx
6sinx cos(x+y) + sinx cos(x+y) = 4sin(x+y) cosx - sin(x+y) cosx
sinx cos(x+y) + sin(x+y) cosx = 5sin(x+y) cosx - 5sinx cos(x+y)
sinx cos(x+y) + cosx sin(x+y) = 5sin(x+y) cosx - 5cos(x+y)sinx
sin(x+x+y) = 5 sin(x+y-x)
sin(x+y) = 5 siny
再问：但是题目的确是这样的呢但是还是谢谢了
再答：推算步骤如上。第一种条件【3tanx=2tan(2x+y)】下，结果是【sin[2(x+y)] = 5 sin(x+y)】第二种条件【3tanx=2tan(x+y) 】下，结果是【sin(x+y) = 5 siny 】

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