tan(α+β)=3/5,tan(β-pai/4)=1/4,则tan(α+pai/4)=?
问题描述：
tan(α+β)=3/5,tan(β-pai/4)=1/4,则tan(α+pai/4)=?
答
tan(α+pai/4)
= tan(α+β - (β-pai/4))
= (3/5 - 1/4)/(1+3/5*1/4)
= 7/20 / 23/20
= 7/23
答
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)]
=(3/5+1/4)/(1+3/5*1/4)
=17/23