已知α是锐角,sin α=1/2.求tan α+1/cot α-1

题目

已知α是锐角,sin α=1/2.求tan α+1/cot α-1

答案

cosα=√[1-(sinα)^2]=√3/2,(α是锐角,是30度）,
tanα=sinα/cosα=√3/3,
cot=√3,
(tan α+1)/(cot α-1)=(3+2√3)/3.