知tan(A-B)/tanA+sin^2C/sin^2A=1求证tanAtanB=tan^2C
问题描述：
知tan(A-B)/tanA+sin^2C/sin^2A=1求证tanAtanB=tan^2C
答
tan(A-B)=(tanA-tanB)/(1+tanA*tanB)tan(A-B)/tanA+sin²C/sin²A=1 左右移项,得 1-[(tanA-tanB)/(1+tanA*tanB)]/tanA=sin²C/sin²A 化简,得 (tan²A*tanB+tanB)/tanA(1+tanA*tanB)=sin²C...