已知tanα=2,sin²α-3sinαcosα+1=

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已知tanα=2,sin²α-3sinαcosα+1=已知tanα=2,sin²α-3sinαcosα+1=已知tanα=2,sin²α-3sinαcosα+1=(sin

已知tanα=2,sin²α-3sinαcosα+1=
已知tanα=2,sin²α-3sinαcosα+1=

已知tanα=2,sin²α-3sinαcosα+1=
(sinα)^2-3sinαcosα+1
=[(sinα)^2-3sinαcosα+(sinα)^2+(cosα)^2]/[(sinα)^2+(cosα)^2]
=[2(sinα)^2-3sinαcosα+(cosα)^2]/[(sinα)^2+(cosα)^2] 分子分母同除(cosα)^2
=[2(tanα)^2-3tanα+1]/[(tanα)^2+1]
=(8-6+1)/(4+1)
=3/5