已知8cos(2x+y)+5cosy=0,且x不等于kx+pi/2,x+y不等于kx+pi/2(k属于Z),求tan(x+y)tanx的值?
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![已知8cos(2x+y)+5cosy=0,且x不等于kx+pi/2,x+y不等于kx+pi/2(k属于Z),求tan(x+y)tanx的值?](/uploads/image/z/6871510-46-0.jpg?t=%E5%B7%B2%E7%9F%A58cos%EF%BC%882x%2By%EF%BC%89%2B5cosy%3D0%2C%E4%B8%94x%E4%B8%8D%E7%AD%89%E4%BA%8Ekx%2Bpi%2F2%2Cx%2By%E4%B8%8D%E7%AD%89%E4%BA%8Ekx%2Bpi%2F2%EF%BC%88k%E5%B1%9E%E4%BA%8EZ%EF%BC%89%2C%E6%B1%82tan%EF%BC%88x%2By%EF%BC%89tanx%E7%9A%84%E5%80%BC%3F)
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已知8cos(2x+y)+5cosy=0,且x不等于kx+pi/2,x+y不等于kx+pi/2(k属于Z),求tan(x+y)tanx的值?
已知8cos(2x+y)+5cosy=0,且x不等于kx+pi/2,x+y不等于kx+pi/2(k属于Z),求tan(x+y)tanx的值?
已知8cos(2x+y)+5cosy=0,且x不等于kx+pi/2,x+y不等于kx+pi/2(k属于Z),求tan(x+y)tanx的值?
8cos(2x+y)+5cosy=0
8cos(2x+y)=-5cosy
8cos[(x+y)+x]=-5cos[(x+y)-x]
8[cos(x+y)cosx-sin(x+y)sinx]=-5[cos(x+y)cosx+sin(x+y)sinx]
8cos(x+y)cosx-8sin(x+y)sinx=-5cos(x+y)cosx-5sin(x+y)sinx
13cos(x+y)cosx=3sin(x+y)sinx
由x不等于k兀+兀/2,x+y不等于k兀+兀/2(k属于Z)
两边同时除以cos(x+y)cosx得
13=[3sin(x+y)sinx]/[cos(x+y)cosx]
13=3*tan(x+y)tanx
tan(x+y)tanx=13/3
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