已知tan a=-1/3,求4sin a-2cos a/5cos a+3sin a=

题目

已知tan a=-1/3,求4sin a-2cos a/5cos a+3sin a=

答案

(4sin a-2cos a)/(5cos a+3sin a)=(4tana-2)/(5+3tana)=(-4/3-2)/[5+3(-1/3)]
=(-10/3)/4=-10/12=-5/6