Tga/tga+ctga-ctga-sin2a

tg a/(tg a+1/tg a)=sin^2 a tg a/(tg^2 a+1)/tg a=sin^2 a tg a*tg a/(tg ^2 a+1)=sin^2 a tg^2 a/(1/cos^2 a)=sin^2 a sin^2 a/cos^2 a*cos^2 a=sin^2 a sin^2 a=sin^2 a