化简：tan(π/8)+1/tan(π/12)

题目

化简：tan(π/8)+1/tan(π/12)

答案

tanα=sinα/cosα
=2s²inα/(2sinαcosα﹚
=[1-cos(2α﹚]／sin﹙2α﹚
∴tan(π/8)=√2-1
1/tan(π/12)=2＋√3
∴tan(π/8)+1/tan(π/12)=√2＋√3＋1