已知:tan(α+β)=2/5,tan(β-π/4)=1/4,则tan(α+π/4)=?

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已知:tan(α+β)=2/5,tan(β-π/4)=1/4,则tan(α+π/4)=?
已知:tan(α+β)=2/5,tan(β-π/4)=1/4,则tan(α+π/4)=?

已知:tan(α+β)=2/5,tan(β-π/4)=1/4,则tan(α+π/4)=?
tan(a+π/4)=tan(α+β-b+π/4)
=tan(α+β-(β-π/4))
=[tan(α+β)-tan(β-π/4)]/[1+tan(α+β)*tan(β-π/4)]
=(2/5-1/4)/(1+2/5*1/4) 分子分母各乘20
= (2/5-1/4)*20/(1+2/5*1/4)*20
=(8-5)/(20+2)
=3/22

,tan(β-π/4)=1/4
tanβ=5/3
tan(α+β)=2/5,
tanα=-19/25
tan(α+π/4)=3/22

tan(a+π/4)=tan【(a+β)-(β-π/4)】
公式展开就可以了


tan(α+π/4)
=tan(α+π/4+β-β)
=tan[(α+β)+(π/4-β)]
=[tan(α+β)+ tan(π/4-β)]/[1-tan(α+β)tan(π/4-β)]
=(2/5-1/4)/(1+2/5*1/4)
=3/22