若2sinα+3cosα=0,则2sin平方α-3 - 知识问答

若2sinα+3cosα=0,则2sin平方α-3sinαcosα+1=?

2个回答

2sinα+3cosα=0
2sinα=-3cosα
tanα=-3/2
tan^2a=9/4
2sin平方α-3sinαcosα+1
=-cos2α-3sinαcosα
=sin^2α-cos^2α-3sinαcosα
=(sin^2α-cos^2α-3sinαcosα)/(sin^2α+cos^2α)
=(tan^2α-1-3tanα)/(tan^2α+1)
=(9/4-1+9/2)/(9/4+1)
=(23/4)/(13/4)
=23/13

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