已知3sinx=sin（2y＋x）,求证tan（x＋y）=2tanyx不等于2k派＋派/2,x+y不等于k派+派/2
问题描述：
已知3sinx=sin（2y＋x）,求证tan（x＋y）=2tany
x不等于2k派＋派/2,x+y不等于k派+派/2
答
3sinx=sin(2y+x)3sin(x+y-y)=sin(y+x+y)3[sin(x+y)cosy-cos(x+y)siny]=sin(x+y)cosy+cos(x+y)sinysin(x+y)cosy=2cos(x+y)sinysin(x+y)/cos(x+y)=2siny/cosytan(x+y)=2tany