sinx=(2tanx/2)/[1+(tanx/2)^2] 怎样证明?

sinx
=sin[2(x/2)]÷1
=[2sin(x/2)cos(x/2)]/[sin²(x/2)+cos²(x/2)]
分子分母同除以cos²(x/2)
=[2sin(x/2)/cos(x/2)]/[sin²(x/2)/cos²(x/2)+1]
=2tan(x/2)]/[tan²(x/2)+1]
=右边
命题得证