tan(x+y)=2tanx(x,x+y≠kπ+π/2,k∈Z),证3siny=sin(2x+y)答对有奖!
问题描述：
tan(x+y)=2tanx(x,x+y≠kπ+π/2,k∈Z),证3siny=sin(2x+y)
答对有奖!
答
记a=x+y,b=xtan(x+y)=2tanxsina/cosa=2sinb/cosb2sinb cosa=sina cosb3siny-sin(2x+y)=3sin(a-b)-sin(a+b)=2sina cosb-4cosa sinb=4sinb cosa-4cosa sinb=03siny=sin(2x+y)