已知sin(x+2y)=3sinx,求tan(x+y)*coty

来源：学生作业帮助网编辑：作业帮时间：2024/11/06 07:39:39

已知sin(x+2y)=3sinx,求tan(x+y)*coty
已知sin(x+2y)=3sinx,求tan(x+y)*coty

已知sin(x+2y)=3sinx,求tan(x+y)*coty
sin(x+2y)=3sinx ,sin[(x+y)+y]=3sin[(x+y)-y] ,sin(x+y)cos(y)+cos(x+y)sin(y)=3[sin(x+y)cos(y)-cos(x+y)sin(y)] ,sin(x+y)cos(y)=2cos(x+y)sin(y) ,tan(x+y)*coty=2

sin(x+y + y) = 3sin(x+y - y)
sin(x+y)cosy + cos(x+y)siny = 3[sin(x+y)cosy - cos(x+y)siny],
4cos(x+y)siny = 2sin(x+y)cosy,
2siny/cosy = sin(x+y)/cos(x+y),
2tany = tan(x+y),
2 = tan(x+y)coty

sin(x+2y)=3sinx
sinxcos2y+cosxsin2y=3sinx（拆开sin(x+2y)）
cos2y+sin2ycotx=3(两边同除以sinx)
1-2(siny)^2+2sinycosycotx=3(拆开cos2y和sin2y)
sinycosycotx=(cosy)^2(移项整理)
sinycotx=cosy
cotx=coty
后面把这个结论带进去就行了。

Tan[x + y]*Cot[y] =
(Sin[x + y]*Cos[y])/( Cos[x + y]*Sin[y]) =
(1/2 (Sin[x] + Sin[x + 2 y]))/(1/2 (-Sin[x] + Sin[x + 2 y])) =
(Sin[x] + Sin[x + 2 y])/ (-Sin[x] + Sin[x + 2 y]) =
(Sin[x] + 3 Sin[x])/ (-Sin[x] + 3 Sin[x]) =
4/2 =
2

已知sin(x+2y)=3sinx,求tan(x+y)*coty 已知sinx=3/5,x∈(π/2,π),求【sin(x+y)+sin(x-y)】/【cos（x+y）+cos（x-y）】的值已知(sinx)2-(siny)2=m求sin(x y)sin(x-y)求sin(x+y)sin(x-y) 已知sinx=1/3,sin(x+y)=1,则sin（2y+x)= 求导数 y=sin^3(2x)+sinx^2 已知sin(x-y)cosx-cos(x-y)sinx=3/5求tan2y的值 sinx=1/3,sin(x+y)=1,求sin（2y+x）=? 已知Sin(x+y)Cosx-Cos(x-x)Sinx=3/5求tan2y的值三角函数最值y=sin^x-3sinx+3/2-sinx三角函数最值y=(sin^x-3sinx+3)/(2-sinx)怎么求? 已知函数y=sin²x+sinx+cosx+2,求函数y的值域已知sinX+cosY=2/3,求3sinX+sin²Y的最大值与最小值已知函数y=sin平方x+2sinx·cosx+3cos平方求y的取值范围 y=sinx,y=sin(t+x)是偶函数,求t 求函数的值域：(1)y=|sinx|-2sinx (2)y=sin|x| |sinx| 求函数的值域：(1)y=|sinx|-2sinx (2)y=sin|x|+|sinx| 已知函数y=-sin^2x+sinx(-π/2 已知2sin平方x-3sinxcosx+cos平方=0 求(cosx-sinx)/(cosx+sinx) 求y=sin^2x+x/sinx的最小值