已知COS(75度+X)=1/3,X为第三象限角,求SIN(X-105度)的值.

cos(x+75)=1/3
sin(x-105)=sin(x-15-90)=-sin[90-(x-15)]=-cos(x-15)
x在第三象限
cos(x+75)>0,所以x+75在第四象限
所以sin(x+75)<0
[cos(x+75)]^2+[sin(x+75)]^2=1
[sin(x+75)]^2=8/9
sin(x+75)=-2√2/3
cos(15-x)=cos[90-(x+75)]=sin(x+75)=-2√2/3
所以sin(x-105)=2√2/3