Question

在△ABC中三边a,b,c满足(a+b+c)(a+b-c)=4/3ab,则tanC等于

Answer 1

根据余弦定理:

2abcosC=a^+b^-c^2=a^2+2ab+b^2-c^2-2ab=(a+b)^2-c^2-2ab=(a+b+c)(a+b-c)-2ab

由:

(a+b+c)(a+b-c)=4/3ab

2abcosC=4/3ab-2ab=-2/3ab;

cosC=-1/3;

tanC^2=sinC^2/cosC^2=(1-cosC^2)/cosC^2=(8/9)/(1/9)=8;

tanC=-2√2;正的舍去