sinB=msin(2A+B) tan(A+B)=3tanA 求m
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sinB=msin(2A+B) tan(A+B)=3tanA 求m
由,tan(A+B)=3tanA
得,sin(A+B)/cos(A+B)=3sinA/cosA
即,sin(A+B)cosA=3cos(A+B)sinA
sinB=sin[(A+B)-A]
=sin(A+B)cosA-cos(A+B)sinA
=3cos(A+B)sinA-cos(A+B)sinA
=2cos(A+B)sinA
sin(2A+B)=sin[(A+B)+A]
=sin(A+B)cosA+cos(A+B)sinA
=3cos(A+B)sinA+cos(A+B)sinA
=4cos(A+B)sinA
由题知,sinB=msin(2A+B)
即,2cos(A+B)sinA=4mcos(A+B)sinA
解得,m=1/2
所以,m的值为1/2
得,sin(A+B)/cos(A+B)=3sinA/cosA
即,sin(A+B)cosA=3cos(A+B)sinA
sinB=sin[(A+B)-A]
=sin(A+B)cosA-cos(A+B)sinA
=3cos(A+B)sinA-cos(A+B)sinA
=2cos(A+B)sinA
sin(2A+B)=sin[(A+B)+A]
=sin(A+B)cosA+cos(A+B)sinA
=3cos(A+B)sinA+cos(A+B)sinA
=4cos(A+B)sinA
由题知,sinB=msin(2A+B)
即,2cos(A+B)sinA=4mcos(A+B)sinA
解得,m=1/2
所以,m的值为1/2
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