tan(π/4+α)×cos2α/2cos²(π/4-α)的值

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
其中
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]/[2cos^2(π/4-α)]
=[(tana+1)/(1-tan²a) × (cos²a-sin²a)]/(cosa+sina)²
=[1/(1-tana) × (cosa-sina)] /(cosa+sina)²
=[cosa/(cosa-sina) × (cosa-sina)]/(c...