已知2cos^2a+3cosasina-3sin^2a=1.求2sina-3cosa/4sina-9cosa.

题目

已知2cos^2a+3cosasina-3sin^2a=1.求2sina-3cosa/4sina-9cosa.

答案

已知2cos^2a+3cosasina-3sin^2a=1.
2cos^2a+3cosasina-3sin^2a
=(2cos^2a+3cosasina-3sin^2a)/(cos^2a+sin^2a) 分子分母同时除以cos^2a
=(2+3tana-3tan^2a)/(1+tan^2a)
=1
所以 2+3tana-3tan^2a=1+tan^2a
4tan^2a-3tana-1=0
(4tana+1)(tana-1)=0
tana=-1/4或tana=1
2sina-3cosa/4sina-9cosa
=(2tana-3)/(4tana-9)
(1) tana=-1/4
(2tana-3)/(4tana-9)=(-1/2-3)/(-1-9)=7/20
(2) tana=1
(2tana-3)/(4tana-9)=(2-3)/(4-9)=1/5