已知锐角a,b满足,sinb=2cos(a+b)sina,求证:tan(a+b)=3tan(a)

已知锐角a,b满足,sinb=2cos(a+b)sina,求证:tan(a+b)=3tan(a)
已知锐角a,b满足,sinb=2cos(a+b)sina,求证:tan(a+b)=3tan(a)

已知锐角a,b满足,sinb=2cos(a+b)sina,求证:tan(a+b)=3tan(a)
sinb=2cos(a+b)sina
3cos(a+b)sina=cos(a+b)sina+sinb=sinacosacosb-(sina)^2sinb+sinb
=sinacosacosb-(cosa)^2sinb
=cosasin(a+b)
两边同除以cos(a+b)cosa
tan(a+b)=3tana
得证