已知@为锐角,且sin^2@-sin@cos@-2cos^2=0 求tan@的值.求sin(@-3.14/3)

已知@为锐角,且sin^2@-sin@cos@-2cos^2=0 求tan@的值.求sin(@-3.14/3)
已知@为锐角,且sin^2@-sin@cos@-2cos^2=0 求tan@的值.求sin(@-3.14/3)

已知@为锐角,且sin^2@-sin@cos@-2cos^2=0 求tan@的值.求sin(@-3.14/3)
sin²a-sinacos-2cos²a=0
等式两边同时除以cos²a
tan²a-tana-2=0
(tana-2)(tana+1)=0
因为tana+1>0
所以tana-2=0,tana=2
sina=2/(根号5),cosa=1/(根号5)
sin(a-pi/3)
=sinacos(pi/3)-cosasin(pi/3)
=1/(根号5)-(根号3/2)(1/(根号5))
=(1-(根号3)/2)/(根号5)