Question

【高中数学】已知AB都是锐角,且A+B≠π/2,(1+tanA)(1+tanB)=2,求证A+B=π/4大神们帮帮忙

Answer 1

(1+tanA)(1+tanB)=2 tanAtanB+tanA+tanB=1 tan(A+B)=(tanA+tanB)/(1-tanAtanB)=1 A+B=π/4+Kπ A+B≠π/2 且A+B