Question

在三角形ABC中,三边a,b,c与面积S满足:S=a^2-(b-c)^2,求tg(B+C)

Answer 1

-8/15.由余弦定理：b^2+c^2-a^2=2bccosA,故S=2bc(1-cosA)=4bcsin^2(A/2)

而S=1/2bcsinA,故联立得tg(A/2)=1/4,故tg(B+C)=tg(180度-A)=-tgA

=-2tg(A/2)/(1-tg^2(A/2))=-8/15