求证:tan(x/2+π/4)+tan(x/2-π/4)=2tanx
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![求证:tan(x/2+π/4)+tan(x/2-π/4)=2tanx](/uploads/image/z/6868237-13-7.jpg?t=%E6%B1%82%E8%AF%81%3Atan%EF%BC%88x%2F2%2B%CF%80%2F4%EF%BC%89%2Btan%28x%2F2-%CF%80%2F4%29%EF%BC%9D2tanx)
求证:tan(x/2+π/4)+tan(x/2-π/4)=2tanx
求证:tan(x/2+π/4)+tan(x/2-π/4)=2tanx
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
求证:tan(x/2+π/4)+tan(x/2-π/4)=2tanx
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