已知tan(a+π/4)=2 求cos2a+3sin²a得值

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已知tan(a+π/4)=2 求cos2a+3sin²a得值

已知tan(a+π/4)=2 求cos2a+3sin²a得值
已知tan(a+π/4)=2 求cos2a+3sin²a得值

已知tan(a+π/4)=2 求cos2a+3sin²a得值
tan(a+π/4)=2
(1+tana)/(1-tana)=2
tana=1/3
cos2a=(1-tan²a)/(1+tan²a)=(1-1/9)/(1+1/9)=4/5
cos2a+3sin²a=cos2a+3/2(1-cos2a)
=3/2-1/2cos2a=3/2-1/2*4/5=11/10
cos2a+3sin²a=11/10

不懂不懂不懂不懂

(1+tana)/(1-tan a)=2. Cos2a+3(sina)^2=(cos a^2+2sin a^2)/(cosa^2-sin a^2). 用齐次方程算,即再除cos a^2,就是关于tan a了