(3) tan(x/2+π/4)+tan(x/2-π/4)
=[tan(x/2)+tan(π/4)]/[ 1-tan(x/2)tan(π/4)]+[tan(x/2)-tan(π/4)]/[ 1+tan(x/2)tan(π/4)]
=[tan(x/2)+ 1]/[ 1-tan(x/2)]+[tan(x/2)- 1]/[ 1+tan(x/2)]
=[(tan(x/2)+ 1)^2-(tan(x/2)- 1)^2]/[ 1-(tan(x/2))^2]
=4tan(x/2)/[ 1-(tan(x/2))^2]
=4tan(x/2)/[ 1-(tan(x/2))^2]=2{tan(x/2)+tan(x/2)/[ 1-(tan(x/2))×(tan(x/2))]}
=2tanx