化简:[tan(π/4+β)-tan(π/4-β)]/tan2β-tan(π/4+β)tan(π/4-β)

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化简:[tan(π/4+β)-tan(π/4-β)]/tan2β-tan(π/4+β)tan(π/4-β)
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化简:[tan(π/4+β)-tan(π/4-β)]/tan2β-tan(π/4+β)tan(π/4-β)
化简:[tan(π/4+β)-tan(π/4-β)]/tan2β-tan(π/4+β)tan(π/4-β)

化简:[tan(π/4+β)-tan(π/4-β)]/tan2β-tan(π/4+β)tan(π/4-β)
可以利用 两角和与差的函数:
tan(A-B)=(tanA-tanB)/(1+tanA*tanB)
转换为:tanA-tanB=tan(A-B)*(1+tanA*tanB)
把 (π/4+β) 看做A  把(π/4-β)看做B
使用此公式后为:
tan[(π/4+β)-(π/4-β)]*[1+tan(π/4+β)*tan(π/4-β)]/tan2β -tan(π/4+β)*tan(π/4-β)]
=tan2β*[1+tan(π/4+β)*tan(π/4-β)]/tan2β -tan(π/4+β)*tan(π/4-β)]
=1+tan(π/4+β)*tan(π/4-β)]-tan(π/4+β)*tan(π/4-β)]
=1