tan(x+y)=2tanx(x,x+y≠kπ+π/2,k∈Z),证3siny=sin(2x+y)答对有奖!

tan(x+y)=2tanx(x,x+y≠kπ+π/2,k∈Z),证3siny=sin(2x+y)答对有奖!
tan(x+y)=2tanx(x,x+y≠kπ+π/2,k∈Z),证3siny=sin(2x+y)
答对有奖!

tan(x+y)=2tanx(x,x+y≠kπ+π/2,k∈Z),证3siny=sin(2x+y)答对有奖!
记a=x+y,b=x
tan(x+y)=2tanx
sina/cosa=2sinb/cosb
2sinb cosa=sina cosb
3siny-sin(2x+y)
=3sin(a-b)-sin(a+b)
=2sina cosb-4cosa sinb
=4sinb cosa-4cosa sinb
=0
3siny=sin(2x+y)