This question contains errors if all the x's are supposed to be the same. Also, sin(x)/cos(x)=tan(x) by definition, so, tan(x) is negative if either sin(x) or cos(x) is negative; tan(x) is positive only if sin(x) and cos(x) are positive or both are negative.
sin(x) and cos(x) are only the same magnitude (disregarding the sign) when the magnitude of x is 45° (positive or negative) and tan(x)=1 or -1.
Perhaps the question should have been sin(x)=½√3, cos(x)=-½, tan(x)=-√3, in which case x=120°.
Or it could have been sin(x)=-½√3, cos(x)=-½, tan(x)=√3, in which case x=240°.