设若α+β=π/3,则tanα+tanβ+根号3*tanα*tanβ的值为

a+b=pi/3
tg(a+b)=(tga+tgb)/(1-tga*tgb)=3^0.5
则tga+tgb=3^0.5(1-tga*tgb)
即tga+tgb+3^0.5*tga*tgb=3^0.5

tan(α+β)=(tanα+tanβ)/(1-tanα*tanβ)
tan(α+β)=tanπ/3=根号3
tanα+tanβ=根号3-根号3*tanα*tanβ
tanα+tanβ+根号3*tanα*tanβ=根号3-根号3*tanα*tanβ+根号3*tanα*tanβ=根号3

a+b=pi/3
tg(a+b)=(tga+tgb)/(1-tga*tgb)=3^0.5
则tga+tgb=3^0.5(1-tga*tgb)
即tga+tgb+3^0.5*tga*tgb=3^0.5

tan(α+β)=(tanα+tanβ)/(1-tanα*tanβ)=根号3
得到tanα+tanβ)=根号3(1-tanα*tanβ) 移项得到tanα+tanβ+根号3*tanα*tanβ的值为根号3