若tan(a+π/8)=2,则tan（a-π/8)=
问题描述：
若tan(a+π/8)=2,则tan（a-π/8)=
答
tan(a-π/8)=tan(a+π/8-π/4)=﹛tan(a+π/8)+tanπ/4﹜/1-tan(a+π/8)tanπ/4=1/3
答
tan(a+π/8)
=tan(a-π/8+π/4)
=[tan(a-π/8)+tan(π/4)]/ [1-tan(a-π/8)tan(π/4)]
=[tan(a-π/8)+1]/[1-tan(a-π/8)]
因为tan(a+π/8)=2
所以[tan(a-π/8)+1]/[1-tan(a-π/8)]=2
所以tan(a-π/8)+1=2-2tan(a-π/8)
解得tan(a-π/8)=1/3