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

Question

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

Answer 1

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