已知tan(a+180/4)=2,则cos2a+3sin^2a+tan2a
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已知tan(a+180/4)=2,则cos2a+3sin^2a+tan2a
![已知tan(a+180/4)=2,则cos2a+3sin^2a+tan2a](/uploads/image/z/18863918-62-8.jpg?t=%E5%B7%B2%E7%9F%A5tan%EF%BC%88a%2B180%2F4%29%3D2%2C%E5%88%99cos2a%2B3sin%5E2a%2Btan2a)
tan(a+Pai/4)=(tana+1)/(1-tana)=2
tana+1=2-2tana
tana=1/3
sina/cosa=1/3
cosa=3sina
(cosa)^2+(sina)^2=1
10sin^2a=1
sin^2a=1/10
cos2a+3sin^2a+tan2a
=cos^2a-sin^2a+3sin^2a+2tana/(1-tan^2a)
=cos^2a+2sin^2a+(2/3)/(1-1/9)
=1+sin^2a+(2/3)/(8/9)
=1+1/10+2/3*9/8
=11/10+3/4
=22/20+15/20
=37/20
tana+1=2-2tana
tana=1/3
sina/cosa=1/3
cosa=3sina
(cosa)^2+(sina)^2=1
10sin^2a=1
sin^2a=1/10
cos2a+3sin^2a+tan2a
=cos^2a-sin^2a+3sin^2a+2tana/(1-tan^2a)
=cos^2a+2sin^2a+(2/3)/(1-1/9)
=1+sin^2a+(2/3)/(8/9)
=1+1/10+2/3*9/8
=11/10+3/4
=22/20+15/20
=37/20
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