已知tan(a-β)=2/5,tan(β-π/4)=1/4,则tan(a-π/4)的值是

问题描述:

已知tan(a-β)=2/5,tan(β-π/4)=1/4,则tan(a-π/4)的值是

tan(a-π/4)
=tan[(a-β)+(β-π/4)]
=[tan(a-β)+tan(β-π/4)]/[1-tan(a-β)+tan(β-π/4)]
=(2/5+1/4)/(1-2/5x1/4)
=(2/5+1/4)/(1-2/5x1/4)
=13/20 / 18/20
=13/18