已知tanα=-1/2,求值1.(sinα+cosα)/(sinα-2cosα)2.(sin^2α-2sinαcosα-4cos^2α)/(3cos^2α-5sin^α)3.1+sin^2α-3sinαcosα
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已知tanα=-1/2,求值
1.(sinα+cosα)/(sinα-2cosα)
2.(sin^2α-2sinαcosα-4cos^2α)/(3cos^2α-5sin^α)
3.1+sin^2α-3sinαcosα
tanα=sinα/cosα=-1/2
cosα=-2sinα
(sinα+cosα)/(sinα-2cosα)
=(sinα-2sinα)/(sinα-4sinα)
=(sinα)/(-3inα)
=-1/3
(sin^2α-2sinαcosα-4cos^2α)/(3cos^2α-5sin^α)
=(sin^2α+4sin^2α-4cos^2α)/(3cos^2α-5sin^α)
=(3sin^2α-4cos^2α)/(3cos^2α-5sin^α)(分子分母同除以cos^2α)
=(3tan^2α-4)/(3-5tan^2α)
=[3*1/4-4]/(3-5/4)
=(-13/4)/(7/4)
=-13/7
sin^2α+cos^2α=1,
1+sin^2α-3sinαcosα
=(1+sin^2α-3sinαcosα)/1 (分子分母同除以cos^2α)
=(1/cos^2α +tan^2α-3tanα)/(1/cos^2α)
=[(sin^2α+cos^2α )/cos^2α +tan^2α-3tanα)]/[(sin^2α+cos^2α )/cos^2α]
=(tan^2α+1+tan^2α-3tanα)/(tan^2α+1)
=(2tan^2α+1-3tanα)/(tan^2α+1)
=12/5
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