Tg a = 2/5 tg b = 1/3 вычислите tg(a+b)

Question

Tg a = 2/5 tg b = 1/3 вычислите tg(a+b)

Answer 1

Tg(a+b)=(tga+tgb)/(1-tgatgb) = (1/3-2)/(1-1/3*(-2))=(-5/3)/(1+2/3) = (-5/3)/(5/3) = -1

ctg(a-b)=1/tg(a-b)=(1+tgatgb)/(tga-tgb) = (1+1/3*(-2))/(1/3+2) = (1-2/3)/( 7/3) = (1/3)/(7/3)=1/7