三角函数简单问题
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解决时间 2021-05-12 03:34
- 提问者网友：溺爱和你
- 2021-05-11 11:21
已知 8*cos（2X+Y）+5cosY=0 求tan(X+Y)*tanX=?
最佳答案
- 五星知识达人网友：雾月
- 2021-05-11 12:53
解： 8cos(2x+y) +5cosy =0
原式=8cos(x+y+x) +5cos(x+y-x) =0
8cos(x+y)cosx -8sin(x+y)sinx + 5cos(x+y)cosx + 5sin(x+y)×sinx =0
整理得:13cos(x+y)cosx = 3sin(x+y)sinx
sin(x+y)sinx/cos(x+y)cosx = 13/3
tan(x+y)tanx = sin(X+y)sinx/cos(x+y)cosx
tan(x+y)tanx = 13/3
原式=8cos(x+y+x) +5cos(x+y-x) =0
8cos(x+y)cosx -8sin(x+y)sinx + 5cos(x+y)cosx + 5sin(x+y)×sinx =0
整理得:13cos(x+y)cosx = 3sin(x+y)sinx
sin(x+y)sinx/cos(x+y)cosx = 13/3
tan(x+y)tanx = sin(X+y)sinx/cos(x+y)cosx
tan(x+y)tanx = 13/3
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