题目

已知sin（a+b）=2/3,sin(a-b)=1/5,求tana*cotb是多少

提问时间：2022-01-21

答案

tan a * cot b = tan a * (1 / tan b) = tan a / tan b = (sin a / cos a) / (sin b / cos b) = sin a * cos b / cos a * sin b ;
sin (a + b) = sin a * cos b +cos a * sin b
sin (a - b) = sin a * cos b - cos a * sin b
1.sin a * cos b = (2/3 + 1/5) /2 = 13/30
2.cos a * sin b = (2/3 - 1/5)/2 = 7/30
:tan a * cot b = 13/7