已知锐角a,b满足,sinb=2cos(a+b)sina,求证:tan(a+b)=3tan(a)
问题描述：
已知锐角a,b满足,sinb=2cos(a+b)sina,求证:tan(a+b)=3tan(a)
答
sinb=2cos(a+b)sina3cos(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)cosatan(a+b)=3tana得证