Find the value oftan(A)+tan(A-120)+tan(240)= ?
Solution :
tan(A-120)=[tan(A)-tan(120)]/[1-tan(A)*tan(120)]=
=[tan(A)+sqrt(3)]/[1+tan(A)*sqrt(3)]
tan(A)+tan(A-120)+tan(240)=tan(A)+sqrt(3)+[tan(A)+sqrt(3)]/[1-tan(A)*sqrt(3)]=[tan(A)-tan^2(A)*sqrt(3)+sqrt(3)-3*tan(A)+tan(A)+sqrt(3)]/[1-tan(A)*sqrt(3)]=
=[-tan^2(A)*sqrt(3)-tan(A)+2*sqrt(3)]/[1-tan(A)*sqrt(3)]=-sqrt(3)*[tan^2(A)+tan(A)/sqrt(3)-2]/[1-tan(A)*sqrt(3)]=
=-sqrt(3)*[tan(A)-2/sqrt(3)]*[tan(A)+3/sqrt(3)]/[1-tan(A)*sqrt(3)]=
=[tan(A)-2/sqrt(3)]*[-tan(A)*sqrt(3)-3]/[1-tan(A)*sqrt(3)] |
