令tanx/2=t
tan(x/2+45)=(t+1)/(1-t)
tan(x/2-45)=(t-1)/(t+1)
tan(x/2+45)+tan(x/2-45)
=[(t+1)^2+(t-1)^2]/(1-T^2)
=4t/(1-T^2)
=2tanx