求证:tan（x/2+π/4）+tan(x/2-π/4)＝2tanx

证明：左边=[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)] (对该式通分后得到下式)
={[tan(x/2) +1 ]² - [tan(x/2) -1 ]²/[1- tan²(x/2)]
=4tan(x/2)/[1- tan²(x/2)] （倍角（半角）公式得到下式）
=2tanx