求证：shx+shy=2sh(x+y/2)ch(x-y/2)
答案:3 悬赏:60
解决时间 2021-02-18 07:18
- 提问者网友：几叶到寒
- 2021-02-17 15:26
求证：shx+shy=2sh(x+y/2)ch(x-y/2)
最佳答案
- 二级知识专家网友：天凉才是好个秋
- 2021-02-17 15:56
左=shx+shy=[e^x-e^(-x)+e^y-e^(-y)]/2
右=2[e^(x+y/2)-e^(-x-y/2)]/2*[e^(x-y/2)+e^(-x+y/2)]/2
=[e^(x)+e^y-e^(-y)-e^(-x)]/2
所以左=右
右=2[e^(x+y/2)-e^(-x-y/2)]/2*[e^(x-y/2)+e^(-x+y/2)]/2
=[e^(x)+e^y-e^(-y)-e^(-x)]/2
所以左=右
全部回答
- 1楼网友：毛毛
- 2021-02-17 16:57
sinx+siny=2sin(x+y/2)cos(x-y/2)
- 2楼网友：长青诗
- 2021-02-17 16:42
shx+shy=(1/2)[e^(x)+e^(y)]+(1/2)[e^(-x)+e^(-y)]
2sh(x+y)/2 ch(x-y)/2=(1/2)[e^(x+y)/2-e^(-x-y)/2]*[e^(x-y)/2+e^(-x+y)/2]
=(1/2)(e^x+e^y)+(1/2)(e^(-x)+e^(-y))=shx+shy
2sh(x+y)/2 ch(x-y)/2=(1/2)[e^(x+y)/2-e^(-x-y)/2]*[e^(x-y)/2+e^(-x+y)/2]
=(1/2)(e^x+e^y)+(1/2)(e^(-x)+e^(-y))=shx+shy
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