tan(π/4+α)=【tan(π/4）+tan(α)】/【1-tan(π/4）*tan(α)】=【1+tan(α)】/【1-tan(α)】
tan(π/4-α)=【tan(π/4）-tan(α)】/【1+tan(π/4）*tan(α)】=【1-tan(α)】/【1+tan(α)】
tan(π/4+α)×cos2α/2cos²(π/4-α)
其中cos2α=sin(π/2-2α）=2sin(π/4-α）cos(π/4-α）带入原式得
tan(π/4+α)× tan(π/4-α)=1
选D
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