已知tana=2,求2⼀3sin^2a-sinacosa+cos^2a的值

2024-12-19 12:15:47
推荐回答(3个)
回答1:

2/3sin^2a-sinacosa+cos^2a
=(2/3sin^2a-sinacosa+cos^2a)/(sin^2a+cos^2a) (sin^2a+cos^2a=1)
=(2/3tan^2a-tana+1)/(tan^2a+1) (上下同时处以cos^2a)
=(2/3*2^2-2/3+1)/(2^2+1)
=3/5

回答2:

(2/3sin^2a-sinacosa+cos^2a)/cos^2a*cos^2a
=(2/3tan^2a-tana+1)*cos^2a
=5cos^2a/3
tana=2
sina/cosa=2
sin^2a/cos^2a=4
(1-cos^2a)/cos^2a=4
cos^2a=1/5
(2/3sin^2a-sinacosa+cos^2a)/cos^2a*cos^2a
=(2/3tan^2a-tana+1)*cos^2a
=5cos^2a/3
=1/3

回答3:

2/3sin^2a-sinacosa+cos^2a
=1/3