tan(X/2+π/4)+tan(x/2-π/4)=2tanx?

问题描述:

tan(X/2+π/4)+tan(x/2-π/4)=2tanx?
难道是题目出错了?
右边题目是2tanx
亲的答案是tan2x?

tan(X/2+π/4)+tan(x/2-π/4)=(tanx/2+1)/(1-tanx/2)+(tanx/2-1)/(1+tanx/2)=[(tanx/2+1)^2-(tanx/2-1)^2]/[(tanx/2+1)(1-tanx/2)]
=4tanx/2/(1-tanx/2^2)
=2(2tanx/2)/(1-tanx/2^2)
=2tanx