已知2tana×sina=3,-π/2<a<0,则cos(a-π/6)=

问题描述:

已知2tana×sina=3,-π/2<a<0,则cos(a-π/6)=

2tana×sina=3
2sin^2a-3cosa=0
2cos^2a+3cosa-2=0
(2cosa-1)(cosa+2)=0
cosa=1/2,a=-π/3,cosa=-2(舍)
cos(a-π/6)= cos(-π/2)= 0