已知非零常数 a,b满足（acosπ/5-bsinπ/5）/（asinπ/5+bcosπ/5）=1/（tan8π/15）,求b/a. 详细过程

题目

已知非零常数 a,b满足（acosπ/5-bsinπ/5）/（asinπ/5+bcosπ/5）=1/（tan8π/15）,求b/a. 详细过程

答案

（acosπ/5-bsinπ/5）/（asinπ/5 bcosπ/5）=1/（tan8π/15）,
左边上下除以a.设b/a=k
cos8π/15sinπ/5＋kcos8π/15cosπ/5=sin8π/15cosπ/5－ksinπ/5cos8π/15
kcos(8π/15－π/5)=sin(8π/15－π/5)
k=-tan(π/3)＝－√3
b/a=-√3