Question

已知a为锐角,且sin^2(a)-sinacosa-2cos^2(a)=0

Answer 1

(1)sin^2(a)-sinacosa-2cos^2(a)=0

等式两边同除于：sin^2(a)得：

1-tana-2tan^2(a)=0

解得：tana=1/2(不合题意的已舍)

由tana=1/2,得：sina=1/√5,cosa=2/√5

sin(a-π/3)=sina*cosπ/3-cosa*sinπ/3

=(1/√5)*(1/2)-(2/√5)*(√3/2)

=(1-2√3)/2√5

=(√5-2√15)/10