题目

已知cos（a-π/6）=12/13且π/6＜a＜π/2,求tana

提问时间：2021-03-01

答案

π/6＜a＜π/2
0＜a-π/6＜π/3
sin(a-π/6)=5/13
sina=sin(a-π/6+π/6)=sin(a-π/6)cos(π/6)+cos(a-π/6)sin(π/6)
=(12+5*3^(1/2))/26
cosa=cos(a-π/6+π/6)=cos(a-π/6)cos(π/6)-sin(a-π/6)sin(π/6)
=(12*3^(1/2)-5)/26
tana=sina/cosa=(12+5*3^(1/2))/(12*3^(1/2)-5)