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

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

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

已知tan(α+β)=2/5,tan(β-π/4)=1/4,求tan(α+π/4)
tan(α+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)
=3/22

tan(θ-δ)
=sin(θ-δ)/cos(θ-δ)
=(sin(θ)cos(δ)-cos(θ)sin(δ)) / (cos(θ)cos(δ)+sin(θ)sin(δ))
分子分母 同除 cos(θ)cos(δ)
=(tan(θ)-tan(δ)) / (1 + tan(θ)tan(δ))
tan(α+π/4)
=tan((α+β) - (...

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tan(θ-δ)
=sin(θ-δ)/cos(θ-δ)
=(sin(θ)cos(δ)-cos(θ)sin(δ)) / (cos(θ)cos(δ)+sin(θ)sin(δ))
分子分母 同除 cos(θ)cos(δ)
=(tan(θ)-tan(δ)) / (1 + tan(θ)tan(δ))
tan(α+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) )
= 3/22

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