已知tan(阿儿法.＋北塔）＝2/5,已知tan(阿儿法＋北他)＝2／5,tan(北他－派／4)＝1/4,则tan(阿儿法＋派／4)=

Question

已知tan(阿儿法.＋北塔）＝2/5,
已知tan(阿儿法＋北他)＝2／5,tan(北他－派／4)＝1/4,则tan(阿儿法＋派／4)=

Answer 1

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)]
=(3/20)/(9/10)
=1/6