Question 1184154
{{{Cos A - Cos B = 1}}} <===> {{{-2Sin((A+B)/2)*Sin((A-B)/2) = 1}}}

{{{Sin A - Sin B = 1/2}}} <===> {{{2Cos((A+B)/2)*Sin((A-B)/2) = 1/2}}}


===> {{{-Sin((A+B)/2)/Cos((A+B)/2) = -Tan((A+B)/2) =  2}}}, after dividing the top equation by the bottom equation.

===> {{{Tan((A+B)/2) = - 2}}}


===> {{{Tan(A+B) = (2Tan((A+B)/2))/(1-Tan^2((A+B)/2)) = (2(-2))/(1-4) = -4/(-3) = highlight(4/3)}}}