求证：tan(x/2+派/4)+tan(x/2-派/4)=2tanx
问题描述：
求证：tan(x/2+派/4)+tan(x/2-派/4)=2tanx
答
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]/[tan(x/2)+1]
={[tan(x/2)+1]^2-[1-tan(x/2)]^2}/[1-tan(x/2)][tan(x/2)+1]
=4tan(x/2)/[1-tan^2(x/2)]
=2tanx