sin(120°-x)=sin120°·cosx-cos120°·sinx;
sin(120°+x)=sin120°·cosx+cos120°·sinx.
由条件“1/sin(120度-x)+1/sin(120度+x)=4根号3/3”得
2·sin120°·cosx=4根号3/3[3/4(cosx)^2-1/4·(sinx)^2]
整理得 4·(cosx)^2-3·cosx-1=0
(4cosx+1)·(cosx-1)=0
∴ cosx=-1/4或cosx=1
sin(120°-x)=sin120°·cosx-cos120°·sinx;
sin(120°+x)=sin120°·cosx+cos120°·sinx.
由条件“1/sin(120度-x)+1/sin(120度+x)=4根号3/3”得
2·sin120°·cosx=4根号3/3[3/4(cosx)^2-1/4·(sinx)^2]
整理得 4·(cosx)^2-3·cosx-1=0
(4cosx+1)·(cosx-1)=0
∴ cosx=-1/4或cosx=1