tan(π/8)+1/(tan(π/12))值,要过程

题目

tan(π/8)+1/(tan(π/12))值,要过程

答案

tan(π/4)=2tan(π/8)/(1-tan(π/8)^2)=1
tan(π/6)=2tan(π/12)/(1-tan(π/12)^2)=(根号3)/3
解二次方程
因为tan(π/8),tan(π/12)＞0
求根公式取正
tan(π/8)=（根号2）-1
tan(π/12)=2-根号3
所以原式=（根号2)-1+1/(2-根号3)
=(根号2)-1+2+根号3
=根号3+根号2+1