sin(2a+b)+2sinb=0 ,求证:tan a =3 tan (a+b)``

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sin(2a+b)+2sinb=0 ,求证:tan a =3 tan (a+b)``

sin(2a+b)+2sinb=0 ,求证:tan a =3 tan (a+b)``
sin(2a+b)+2sinb=0 ,求证:tan a =3 tan (a+b)
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sin(2a+b)+2sinb=0 ,求证:tan a =3 tan (a+b)``
sin(2a+b)=sin(a+b)*cosa+sina*cos(a+b);
sinb=sin(a+b-a)=sin(a+b)*cosa-cos(a+b)*sina;
代入sin(2a+b)+2sinb=0 :
3*sin(a+b)*cosa-cos(a+b)sina=0;………………(*)
只要cosa与cos(a+b)不为0,由(*)式可得结论.