若tan(α+β)=2/5.tan(b-π/4)=1/4.则tan(a+π/4)等于
问题描述:
若tan(α+β)=2/5.tan(b-π/4)=1/4.则tan(a+π/4)等于
答
tan(a+π/4)=tan[(a+b)-(b-π/4)]
=[tan(a+b)-tan(b-π/4)]/[1-tan(a+b)tan(b-π/4)
=(2/5-1/4)/(1-2/5*1/4)
=(8-5)/(20-2)
=3/18
=1/6