(sin (30°+a) -cos (60°+a) / (sin (30°+a)+cos (60°+a)

sin (30°+a) -cos (60°+a) / (sin (30°+a)+cos (60°+a)=(sin30cosa+cos30°sina) — (cos60°cosa-sin60°sina) \ (sin30cosa+cos30°sina)+(cos60°cosa-sin60°sina)=(1/2cosa+\frac{\sqrt{3}}{2} sina) — (1/2cosa- \frac{\sqrt{3}}{2} sina) \ (1/2cosa+\frac{\sqrt3}{2} sina)+(1/2cosa- \frac{\sqrt3}{2} sina)=\sqrt{3} sina\cosa=\sqrt{3}tga