1+tanx·tanx/2=2cosx·tanx/sin2x求证

sin2x/2cosx (1+tanx*tanx/2)
=2sinxcosx/2cosx (1+tanx*tanx/2)
=sinx/(1+tanx*tanx/2)
因为tan2α=2tanα/[1-(tanα)^2]
所以,tanx=(2tanx/2)/[1-(tanx/2)^2]
1+tanx*tanx/2=1+{(2tanx/2)^2/[1-(tanx/2)^2]}
={1+(tanx/2)^2}/[1-(tanx/2)^2]
=1/cosx
即：1+tanx·tanx/2=2cosx·tanx/sin2x