tanA+tanB+tanC=3√3 (tanB)^2=tanAtanC 求∠B
问题描述:
tanA+tanB+tanC=3√3 (tanB)^2=tanAtanC 求∠B
答
∵tanA+tanB+tanC=tan(A+B)×(1-tanAtanB)+tanC =tan(180°-C)×(1-tanAtanB)+tanC =-tanC×(1-tanAtanB)+tanC =-tanC×1+tanAtanBtanC+tanC =tanAtanBtanC =3√3 ∴tanAtanC=3√3/tanB 又∵tan^2B =tanAtanC ∴ta...